What do Protestants say was the source for the doctrine of the perpetual virginity of Mary?

Numerous Church Fathers have interpreted Ezekiel 43:27-44:4 as referring to the perpetual virginity of Mary:

And when these days are expired, it shall be, that upon the eighth day, and so forward, the priests shall make your burnt offerings upon the altar, and your peace offerings; and I will accept you, saith the Lord GOD. Then he brought me back the way of the gate of the outward sanctuary which looketh toward the east; and it was shut.

Then said the LORD unto me: This gate shall be shut, it shall not be opened, and no man shall enter in by it; because the LORD, the God of Israel, hath entered in by it therefore it shall be shut.

It is for the prince; the prince, he shall sit in it to eat bread before the LORD; he shall enter by the way of the porch of that gate, and shall go out by the way of the same. Then brought he me the way of the north gate before the house: and I looked, and, behold, the glory of the LORD filled the house of the LORD: and I fell upon my face.

These include the eastern Father, Cyril of Alexandria¹ (ca 378-444), and the western Fathers Jerome² (ca 347-420), and Ambrose³ (ca 337-397), who were followed later by Augustine⁴ (ca 354-430)

The Church Fathers have various degrees of standing among Protestants, but even Protestant commentators have supported this explanation in their writings. John Gill (ca 1697-1771), an English Baptist theologian, wrote, for example:

Various are the sentiments of expositors concerning this gate. Some of the ancients have interpreted it of the Virgin Mary, by whom Christ came into this world in human nature, being born of her, a virgin, who had never known man, and as is thought never did after the birth of Christ; nor were any afterwards born of her; no man might come into the world by her, by that self-same way the incarnate God did, and for that reason. This sense is approved of, not only by Papists, but by many Protestant writers.⁵

<sup>1. Commentary on Luke, Sermon I
2. Letter XLVIII.21, Against Pelagius
3. Letter XLIV
4. On the Annunciation
5. Exposition on the Whole Bible</sup>

One of the defining tenets of Protestant Christianity is sola scriptura--that the Scriptures are the fundamental basis for all doctrine. This is in contrast to extra-biblical teachings. The idea is that if it were important enough for us to know, God would have told us in the Scriptures themselves and not have us rely on extra-biblical teachings. Protestants see the potential for great danger when there is reliance on the teaching of men rather than on the unchanging Word of God.

To answer your question specifically, Protestants generally believe that this was a teaching that was introduced by the Catholic church centuries after the life of Jesus. There is no apostolic authority behind it, as it appears nowhere in Scripture. All we are told is that Mary was a virgin at Jesus' conception and remained so until His birth, as @ryanOptini also noted.

Then Joseph being raised from sleep did as the angle of the Lord had bidden him, and took unto him his wife, and knew her not till she had brought forth her firstborn son: and he called his name Jesus. Matthew 1:24-25

Nowhere in Scripture does it indicate that Mary remained a virgin after the birth of Christ. This would certainly have been noteworthy, since it would not have been a normal thing for a married woman (and man, for that matter) to not have a consummated marriage and experience the normal and sacred aspects of marriage. Yet, the best biblical support is quite vague at best.

It is also problematic to Protestants as to why it would have been necessary for Mary to remain a virgin--and for Joseph to remain celibate towards her as her husband. Why is this level of intimacy denied both Mary and Joseph and what could possibly be wrong with it?

Now, it may have been the Mary began to be held up as a female example for women to follow. Men could look to Jesus Himself or any of the apostles to see a male example to follow. So, perhaps it was well-intentioned. God found favor with Mary, much like He had done with Noah in the Old Testament. Her virginity as an unmarried woman is commendable as well. And perhaps over time, Mary's virginity was turned into eternal virginity to really set her apart and give her even more honor.

Summary

So, again, it may have been well-intentioned, but Protestants generally believe it was a teaching introduced by the Catholic church long after the apostles were gone. So, the teaching lacks apostolic authority as well as biblical support, which is extremely important if something so unexpected is to be believed and held as such an important doctrine.

One answer that has been suggested is the Infancy Gospel of James (AKA The Protoevangelium of James). This document dates to roughly the middle of the second century and focuses largely on the person of Mary from her birth to the birth of Jesus. As the central character, Mary's honor and purity are defended in great detail. Mary's virginity is repeatedly demonstrated—including when she is six-months pregnant and endures an ordeal by the high priest. Since she survives drinking poison, the priest says, "If the Lord God has not made manifest your sins, neither do I judge you."

Most important to our question comes immediately after the miraculous birth of Jesus:

And the midwife went forth out of the cave, and Salome met her. And she said to her: "Salome, Salome, I have a strange sight to relate to thee: a virgin has brought forth—a thing which her nature admits not of." Then said Salome: "As the Lord my God liveth, unless I thrust in my finger, and search the parts, I will not believe that a virgin has brought forth."

And the midwife went in, and said to Mary: "Show thyself; for no small controversy has arisen about thee." And Salome put in her finger, and cried out, and said: "Woe is me for mine iniquity and mine unbelief..."—Roberts-Donaldson English Translation (with added punctuation)

In other words, the midwife and Salome are said to have inspected Mary's hymen immediately after the birth in order to show that Mary was a virgin before and after the event.

So here's my speculative sequence of events:

1. Jesus was born from the virgin Mary as described in Luke and Matthew.
2. Sometime later, opponents of Christianity questioned this doctrine.
3. In response, someone (no scholars believe it was written by James the Just) wrote the Infancy Gospel to defend Mary's honor.
4. Even though it was not accepted as canonical, many early Christians accepted the story of Mary's perpetual virginity and even expanded on it. (The Protoevangelium does not speak of Mary's life after the birth of Jesus, so it doesn't claim she never had other children.)
5. The doctrine of the perpetual virginity of Mary became enshrined in tradition.

When the Reformation examined church tradition against scripture, it understandably focused on what it considered most important and Mariology was not high on the list. Therefore, the question of whether Mary remained a virgin after Jesus' birth was not immediately questioned.

I should point out that as far as it goes, perpetual virginity is an innocuous doctrine to the Protestant worldview. That Christ was born of a virgin is a matter asserted by the earliest Creeds and the gospels themselves, so it wouldn't be much of a stretch if it turned out that Mary remained a virgin—what's a little more miracle after all? But Protestants generally agree that perpetual virginity is a) not true and b) part of a larger set of doctrines that misplace the importance of Mary. That's why we tend to be opposed to the doctrine.

As you point out, pre-Reformation Christians did read scripture. But they did not have many of the tools of criticism that were developed at about the same time. Therefore, the doctrine of perpetual virginity was placed beside the gospel accounts and the differences were harmonized. The harmonized interpretation then became part of church's tradition. When the doctrine of sola scriptura was introduced, the differences were interpreted as denying perpetual virginity, which was therefore dropped. It's not necessarily even a matter of Protestants being better at interpretation. Rather, I would say that Protestants are more willing to be skeptical of tradition.

Summary

If Protestants venture any theory at all, it is that perpetual virginity defense entered the church's tradition very early on in its history in response to charges that Christ's birth was entirely natural (and even illegitimate). Understandably, the tradition may have exaggerated the facts at times.