For Protestantism to make much sense, the Church must have, at some point, abandoned the truth and become apostate. Otherwise, Protestantism has no license to exist. But when was this “Great Apostasy”? Protestants offer varying opinions, but none of them hold up to scrutiny.
Was it right after the deaths of the Apostles?
A view most supported by Mormons and Jehovah’s Witnesses is that, after the Apostles, the Church quickly fell into apostasy. This would be a massive blow at both God’s promise to guard His Church (Joshua 1:5; Matthew 16:18) and all of the doctrine mentioned hereafter. But if this were true, would not one of the disciples of the Apostles have spoken out? We have writings from many of them, including Pope St. Clement I, St. Barnabas, St. Polycarp, and St. Ignatius of Antioch. None of them mention a “Great Apostasy”. But even if we indulge the other side and admit the possibility that even these men fell away, we still have early documents and creeds (like the Didache) that were probably formulated under the authority of the Apostles. Because Christians continued to be in accord with these extra-Biblical teachings, we know that they must have been in accord with the true Church.
Was it at the time of Constantine?
A semi-popular view is that Constantine corrupted Christianity by encouraging “pagan” elements and demanding a decision from the First Council of Nicaea. This is the view that I come into contact with most often, but it is also the most problematic. If the Church became apostate by 337 (the year of Constantine’s death), then the Biblical canon – which only really started to be compiled by St. Athanasius in 367 – may be wrong: we would have no assurance of its infallibility. Also, on top of that, all later theology would be necessarily nulled.
Was it during the Middle Ages?
The possibility of an apostasy in Medieval times seems far-fetched, too. This theory revolves, primarily, around hatred for some “bad” popes. Rather than focusing on doctrinal issues, proponents of this theory typically resort to character defamation. Many attack the Crusades, which tamed a fanatic Islam, and such. But in this period, literacy rates increased, art flourished, the university system developed, laws were better-codified, and the Bible became more accessible to lay people [1, 2]. The only seemingly objectionable doctrinal development was Pope Boniface VIII’s declaration, “Outside of the Church, there is neither salvation nor the remission of sins”, but even this originates with St. Cyprian! The teaching relates to: 1) the fact that baptism (whether by water, blood, or desire) brings one into the Church (even if done within a Protestant community), because the sacrament was entrusted to Her and She allows anyone with the right intent to perform it, and 2) the importance of conscience and the dangers of apostasy. Nothing worthy of damnation here!
Was it just before the “Reformation”?
The idea of a “restoration” being needed just before the “Reformation” also seems improbable. This common idea is based on the “selling” of indulgences [1, 2, 3] (Martin Luther attacks the practice multiple times in his Ninety-Five Theses), but is mostly due to a misunderstanding. Again, the Protestant understanding usually relies on the assault of characters: people like Johann Tetzel are demonized — perhaps rightfully — for abusing the system. But this abuse was not a doctrinal problem of the Church; rather, it was a disciplinary problem of men. Indulgences simply remove the temporal punishment due for past sin — they are not a “Get out of Hell free” card — and even when they were “sold,” they required some sort of penance. Indulgences only have a salvatory effectiveness (remittance of time in Purgatory) if the recipient is already destined for Heaven. So, it would seem that the fuss is all about nothing.
In conclusion, I see none of these options as likely.
Martin Luther said and wrote many heretical things, but here are a mere five quotes, along with Biblical passages that disprove them.
1. “For reason is directly opposed to faith. This is why you must let reason go. It must be killed and buried in believers.” 
(Answer: Proverbs 14:15, Colossians 1:9, Colossians 4:5-6, 1 Thessalonians 5:19-22)
2. “..[A Christian] could not lose his salvation, however much he sinned, unless he refused to believe. For no sin can condemn him save unbelief alone.” 
(Answer: Hebrews 10:26-27)
3. “Be a sinner, and let your sins be strong, but let your trust in Christ be stronger, and rejoice in Christ who is the victor over sin, death, and the world. We will commit sins while we are here, for this life is not a place where justice resides. …No sin can separate us from Him, even if we were to kill or commit adultery thousands of times each day.” 
(Answer: Psalm 4:4, Matthew 5:48, Hebrews 10:26-27)
4. “It is good that we have such a man [Jesus Christ], because God in himself is cruel and bad.” 
(Answer: Psalm 51:1, Jeremiah 9:24, Jeremiah 31:3)
5. “I miss more than one thing in this book [Revelation, aka Apocalypse], and this makes me hold it to be neither apostolic nor prophetic…and [I] can nohow detect that the Holy Spirit produced it. …My spirit cannot fit itself into this book.” 
(Answer: Revelation 22:19)
1. Luther’s Sermon on Matthew 19:13-15. “What Luther Says,” 1:485-486 (entry 1440). [link]
3. Let Your Sins Be Strong: A Letter From Luther to Melanchthon. Translated by Erika Bullmann Flores. [link]
5. M. Reu, Luther’s German Bible: An Historical Presentation Together with a collection of Sources (Ohio: The Lutheran Book Concern, 1934) 174-175 [link]