A possible explanation is simply that not all prophecies come true. For Paul it was not a question of cessationism vs. continuationism. It was simply that, especially in Paul's concept of prophecy, prophetic utterances do not always come to pass. Lest it be objected that I am not answering the question, I point out that the main question says only "what is meant" by the verse, not which group is right or wrong in their interpretation.
If we look at the OT, a well known example is the story of Jonah, who was instructed by God to prophesy the destruction of Nineveh with 40 days. Jonah actually pouted when his prophecy did not prove true. Jeremiah established this principle of prophecies failing more directly when he declared:
If at any time I (God) declare concerning a nation or a kingdom, that I will
pluck up and break down and destroy it, and if that nation,
concerning which I have spoken, turns from its evil, I will repent of
the evil that I intended to do to it. (18:7-8)
We should also consider that Paul's concept of prophecy may not be the same as what we presume. For example he said "prophecy is not for unbelievers but for believers." (1 Corinthians 14:22) Paul is not dealing with a situation where prophecy is issued by a solitary figure, as in a OT book, where the prophets not only proclaimed God's will for the people of Israel but also declared oracles against "the nations." Indeed prophecy at Corinth seems to be ubiquitous and even chaotic, just as with the gift of tongues earlier in the chapter. Thus Paul says:
Let two or three prophets speak, and let the others weigh what is
said. If a revelation is made to another sitting by, let the first be
silent. For you can all prophesy one by one, so that all may learn and
all be encouraged... God is not a God of confusion but of peace.
Given a situation where prophets do not even wait their turn to speak, we can envision that not every supposed prophecy would come to pass. This does not mean those whose prophecies failed were "false prophets" but simply that they one not 100 percent accurate. We get a sense of the in Deut. 18:
When the prophet speaks in the name of the Lord, and the thing does
not happen or come true, that is the thing which the Lord has not
spoken. The prophet has spoken it presumptuously.(18:22)
Note that not all such prophets are denounced as "false prophets." In some cases they may be sincere, but not on target. They have confused God's voice and their own thoughts. Just as Jesus said "you will know them by their fruits," Dt. teaches they will be known by whether their prophecy comes true. This may be the case with the prophets of the Corinthian church.
Turning to "when that which is perfect is come," this too needs to be understood in the context of the rest of chapter.
When I was a child, I spoke like a child, I thought like a child, I
reasoned like a child; when I became a man, I gave up childish ways.
For now we see in a mirror dimly, but then face to face. Now I know
in part; then I shall understand fully, even as I have been fully
understood. So faith, hope, love abide, these three; but the greatest of these is love.
Paul is reacting to an immature Corinthian congregation which which tongue-speaking and prophecy are messy and disorderly, and love sometimes gets lost in the shouting. He wants true prophecy that does not create confusion and where prophets treat each other politely. Truth will be known in time, and true prophets will be known by their fruits. That which is imperfect will pass away as the true prophecy becomes clear.
This issue is best understood in the context of the immediate situation Paul dealt with, not in the context of the later controversy over whether prophecy would continue beyond a certain point in the church's development.