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Note: All emphasis in the quotes from Ellen G. White Writings (both the underlining and the occasional bolded text), has been added. Also, unless otherwise stated, Bible quotations are from the NASB with all emphasis added)
The Shut Door Doctrine
The Metamorphosis of The Shut Door Doctrine
Ellen White's Shut Door Visions
An Extremely Tenuous Defense
So When Does The Door Actually Shut?
The Shut Door Doctrine
As said in a previous chapter, the Seventh Day Adventist pioneers taught the "shut door" doctrine from 1844 to about 1850 or 1851. Anyone who had not accepted the Adventist message by the time Jesus entered the Holy of Holies in 1844 was permanently 'shut out' and had no hope of being saved, thus Adventists no longer needed to work for the salvation of the world.
In January, 1845, Ellen Harmon began visiting the little advent bands in Maine and New Hampshire to tell them what she had seen in vision. Concerning her ministry at this time, Otis Nichols wrote William Miller:
"Her message was always attended with the Holy Ghost, and wherever it was received as from the Lord, it broke down and melted their hearts like little children, fed, comforted, strengthened the weak, and encouraged them to hold on to the faith, and the seventh month movement, and that our work was done for the nominal church and the world, and what remained to be done was for the household of faith." 
The Metamorphosis of The Shut Door Doctrine
The belief that the probationary period had come to an end and there was no more mercy for sinners gradually changed over time. According to Present Truth Magazine (Emphasis Added)
"Although they believed that the ministry of Christ in the most holy place was not available to those who had rejected the October 22 message, the pioneers - including Ellen G. White - progressively modified their shut-door position. This metamorphosis took about ten years. 
This was substantiated by Arthur White in Ellen G. White And The Shut Door Question. (All Emphasis Added)
Seventh-day Adventist pioneers did for some time hold shut door views. What the careful student soon discovers is that the meaning and significance of the term "shut door" underwent a marked change between 1844 and 1851... Adventists came up to 1844 expecting that the Lord would then appear and probation close for all mankind. For a brief period following October 22, those who did not at once repudiate their former faith still held that probation had closed and that there was no more mercy for sinners.
He added that Sabbatarian Adventists
".. soon came to realize that Christ was now ministering in heaven above in the second phase of His High Priestly ministry--that He had shut the door of the first apartment and had opened the door to the second or Most Holy Place, and they were to announce this grand transition to all who would hear. The door was still open to those who had not willfully rejected the judgment-hour message, children who had not then reached the age of accountability, and those in the churches who were still honest in heart 
Almost 40 years later (in 1883), By way of explaining how the "shut door' idea was initially viewed, Ellen White wrote that their belief that the door of mercy was forever closed to the world was prior to her first vision. But now that God had corrected their error (I have to wonder what took Him so long), they understood that only those who either willfully rejected the light from heaven, or initially accepted - but subsequently renounced the message, were left in darkness.
For a time after the disappointment in 1844, I did hold, in common with the Advent body, that the door of mercy was then forever closed to the world. This position was taken before my first vision was given me. It was the light given me of God that corrected our error, and enabled us to see the true position. I am still a believer in the shut-door theory, but not in the sense in which we at first employed the term or in which it is employed by my opponents. 
In response to an 1874 editorial published by Adventist Miles Grant, which included a number of witnesses who testified that Ellen White taught that no genuine conversions were made after 1844, she responded
With my brethren and sisters, after the time passed in forty-four I did believe no more sinners would be converted. But I never had a vision that no more sinners would be converted. 
However, in spite of her claims to the contrary, at least two of Ellen White's earlier visions supported the shut door doctrine.
Ellen White's Shut Door Visions
December, 1844 Vision
It seems reasonably clear that Ellen White's very first vision supported a version of the 'shut door' position. Note: James White dates the vision to December of 1844 . Because the written description of this vision is a very long one, I will only give the gist of the relevant sextion.
In essence, she saw the "advent people" traveling a narrow, but brightly lit, path to city at its end. This path was high above the world, and the travelers were safe as long as they kept their eye on Christ. However, when some of them claimed that it was "not God that had led them out so far", the light behind them went out, leaving their feet in "perfect darkness", and they fell off the path down into the dark and wicked world below.
She then added
It was just as impossible for them to get on the path again and go to the City, as all the wicked world which God had rejected". 
God apparently not only rejected backsliding Adventist, but all the wicked world as well which certainly sounds like He had shut the door very firmly indeed
February, 1845 Vision
On February, 15, 1846 Ellen White wrote to a "Bro. Jacobs" who had published an account of a vision given her one year earlier, asking him to publish some important things which had been left out of the earlier version. One wonders why Ellen White waited an entire year before requesting the Day-Star to print the entire vision. Whatever the reason, the following is an excerpt from the version printed the following month, on March 14, 1846. (Emphasis Added)
I saw the Father rise from the throne, and in a flaming chariot go into the holy of holies within the veil, and sit down. Then Jesus rose up from the throne, and the most of those who were bowed down arose with Him. I did not see one ray of light pass from Jesus to the careless multitude after He arose, and they were left in perfect darkness. Those who arose when Jesus did, kept their eyes fixed on Him as He left the throne and led them out a little way... Then a cloudy chariot, with wheels like flaming fire, surrounded by angels, came to where Jesus was. He stepped into the chariot and was borne to the holiest, where the Father sat. 
In a letter to Bates she gives the setting of this vision. Although Ellen White didn't include many details, it certainly caused other to believe in the shut door position,
"The view about the Bridegroom's coming I had about the middle of February, 1845. (All Emphasis Added)
While in Exeter, Maine, in meeting with Israel Dammon, James, and many others, many of them did not believe in a shut door. I suffered much at the commencement of the meeting... It was then I had a view of Jesus rising from His mediatorial throne and going to the Holiest as Bridegroom to receive His kingdom. They were all deeply interested in the view. They all said it was entirely new to them... When I came out of vision, my ears were saluted with Sister Durben's singing and shouting with a loud voice. Most of them received the vision, and were settled upon the shut door. Previous to this I had no light on the coming of the Bridegroom, but had expected Him to [come to] this earth to deliver His people on the tenth ay of the seventh month. I did not hear a lecture or a word in any way relating to the Bridegroom's going to the Holiest. 
Additionally, in recounting another vision dated 1849, she said
My accompanying angel bade me look for the travail of soul for sinners as used to be. I looked, but could not see it, for the time for their salvation is past. 
Her husband, James White, was like minded. On page 69 of the April 1850 edition of Present Truth, he wrote
Babylon, the nominal church is fallen. God's people have come out of her. She is now the 'synagogue of Satan' (Rev. 3:9). 'The habitation of devils, and the hold of every foul spirit, and the cage of every unclean and hateful bird' (Rev. 18:2)." (Present Truth, April, 1850. Pg. 69)
How is it possible that a "prophet" of God got such an important detail wrong? No Old or New Testament doctrines were ever modified, much less over the long period of about ten years.
An Extremely Tenuous Defense of the Metamorphosis of The Shut Door Doctrine
In light of when the Bible tells us when exactly the doors of mercy will forever close (See below), Ellen White's 1844-1845 visions alone should be enough to label her a false prophet and move on. However, she is defended to the death by believers in her prophetic authority. Unfortunately, many of the defensive arguments put forth by Seventh Day Adventists are without merit and some, like the one below, simply compound the original errors.
In his book More Than a Prophet, Graeme Bradford, professor from the Theology Department of Avondale College and a firm believer in the genuineness of Ellen White's prophecies, says (Emphasis Added)
In the early years of her ministry she, along with others, taught that the door of opportunity was closed to all who had not accepted the preaching of the Millerites regarding the soon coming of Jesus. She was part of the "Shut Door Adventist" group that emerged out of the Millerite movement. We have to bear in mind that prophets do not always understand what God is revealing to them in vision. We have already noticed that Peter pondered in his heart what the vision on the rooftop at Joppa was meant to convey to him. Subsequent experience at the home of a Gentile made it clear that he was to treat the Gentiles as equals with the Jews. 
It is true that prophets "do not always understand what God is revealing to them in vision" and Peter was no exception. However, the Bible does not say that he 'pondered' anything but was very perplexed, which is no wonder considering how symbolic his vision was. But Peter wasn't confused for very long. if you read Acts 10 and 11, the men sent to fetch Peter stayed with him overnight and, on the next day, accompanied him to Cornelius' house in Caesarea where he immediately discovered what the vision meant.
In a footnote, Graeme Bradford says
"... a similar "Shut Door teaching" was applied by early Christians (including Peter) for the first 10 years of the existence of the newly formed Christian Church. For the first 10 years they only preached to the Jews as being worthy of God's grace. That is the purpose of the vision given by God to Peter in Acts 10: 9-34. All movements raised up by God still have the imperfections common to humanity 
It is true that the early apostles did not initially preach to the Gentiles.
However, this was not an "imperfection" of the movement or any misunderstanding on their part. Jesus told them not to go by way of the Gentiles but to "the lost sheep of the house of Israel" (Matthew 10:5-6) simply because God always intended for the Jews to hear first. Not only were they the chosen people and the guardians of God's word, but Jesus was Himself a Jew (salvation is from the Jews). Being saved means being connected by faith to Abraham and the covenant God made with him.
Although the apostles did not know this until Peter's vision, God's salvation plan was always meant to be extended to all men. As Jesus Himself said
I have other sheep, which are not of this fold; I must bring them also, and they will hear My voice; and they will become one flock with one shepherd. (John 10:16 NASB)
There is a huge difference between God revealing His plan in stages, and doctrines that change over the years.
So When Does The Door Actually Shut?
Ellen White says
There was a shut door in Christ's day. The Son of God declared to the unbelieving Jews of that generation, "Your house is left unto you desolate" (Matthew 23:38). 
Reading this in context - Jesus wanted to gather His children under His wing but they were unwilling to come. While it is true that anyone who is unwilling to be saved is going to be left desolate, the question is when this actually happens.
Apparently no one in the 19th century (and few today) seem to have come to any understanding of when the door to salvation finally closes. The Scriptures tell us in no uncertain terms exactly when this happens without the necessity of complex unbiblical theories or prophecies. Read Revelation 10.
(5) Then the angel whom I saw standing on the sea and on the land lifted up his right hand to heaven, (6) and swore by Him who lives forever and ever, who created heaven and the things in it, and the earth and the things in it, and the sea and the things in it, that there will be delay no longer, (7) but in the days of the voice of the seventh angel, when he is about to sound, then the mystery of God is finished, as He preached to His servants the prophets. (Revelation 10:5-7 NASB)
The mystery of God finishes as the seventh angel is about to sound. In other words, the mystery of God will be complete before the blowing of the seventh trumpet.
But what is this mystery? We usually think of a mystery as something that we have to figure out. For example a murder mystery is a "whodunit". However, when the Bible speaks of a "mystery", it does not mean something that is difficult to understand, or even incomprehensible. In Scripture, the word refers to something that had not previously been revealed... ie. the good news of the Gospel that God planned "before the ages". A believer understands the mystery (which is precisely why they became believers), but others do not.
but we speak God's wisdom in a mystery, the hidden wisdom which God predestined before the ages to our glory; the wisdom which none of the rulers of this age has understood; for if they had understood it they would not have crucified the Lord of glory; (1 Corinthians 2:7-8 NASB)
and to bring to light what is the administration of the mystery which for ages has been hidden in God who created all things; (Ephesians 3:9 NASB)
that is, the mystery which has been hidden from the past ages and generations, but has now been manifested to His saints, (Colossians 1:26 NASB)
Jesus said to his disciples...
And He was saying to them, "To you has been given the mystery of the kingdom of God, but those who are outside get everything in parables, (Mark 4:11 NASB)
And the disciples came and said to Him, "Why do You speak to them in parables?" Jesus answered them, "To you it has been granted to know the mysteries of the kingdom of heaven, but to them it has not been granted. (Matthew 13:10-11 NASB)
So when the mystery of God comes to an end, the doors to the Kingdom close forever and there will be no possibility of redemption for any that have not yet become a disciple of the Lamb.
The doors will not shut one second before the angel prepares to sound that last and final trumpet.
However, there is more to this last Trumpet which is, in a sense, the most eventful of all the trumpets, since it literally ushers the old age out, and the new one in. It not only signals the close of the doors of the Kingdom, but also
a) Marks the point when believers are caught up in the clouds to meet the Lord in the air (the rapture). The dead will rise first, followed by those still alive at this point. Note: "sons of the kingdom", as they are called, are physically moved off the earth for a very specific reason.
b) Introduces the Seven Bowls that signify the end of all things..
See The End Of The Age Part IV... The Seventh Trumpet
Continue on To Chapter 5. Was Ellen White a True Prophetess?
End Notes. The Shut Door Doctrine
 Ellen G. White Writings. Otis Nichols to William Miller, April 20, 1846, White Estate Document File #439b.
 "1844" Re-Examined. Section 7. The Shut Door and Ellen G. White. http://www.presenttruthmag.com/7dayadventist/1844/7.html
 Arthur White. Ellen G. White And The Shut Door Question. A Review of the Experience of Early Seventh-day Adventist Believers in its Historical Context. http://www.whiteestate.org/issues/shut-alw.html
 Ellen G. White Writings. Ellen G. White, Selected Messages, book 1, p. 63.
 Ellen G. White Writings. Ellen White. Messenger of the Lord, Page 562.
 Ellen G. White Writings. 101 Questions on the Sanctuary and on Ellen White, Page 57.
 Ellen G. White Writings. Ellen White: The Early Years: 1827-1862 (vol. 1), Page 56-57. The First Vision as Published in the Day-Star http://text.egwwritings.org/publication.php?pubtype=Book&bookCode=1BIO&pagenumber=56¶graphReferences=1
 Ellen G. White Writings. Ellen White. March 14, 1846, Page 55.
 Ellen G. White Writings. Ellen White and the Shut Door Question, Page 25.
 Ellen G. White Writings. Present Truth, pp. 21- 22, August, 1849
 Graeme Bradford. More Than a Prophet. Chapter Fourteen.. Ellen White's Spiritual Growth. Signs of a Maturing Ministry.
 Ellen G. White Writings. Selected Messages Book 1, Page 63.