The philosophy seems to have continued strong into about the 3rd century AD. Thereafter, it went into decline. By the middle of the 6th century, when the Emperor Justinian closed all the philosophical schools in Athens and dispersed the teachers, Epicureanism appears to have been already dead.
The main traditions of thought during the last few centuries of the ancient world were turned away from the everyday world. There were the neoplationists, with their settled belief in a higher reality that could be approached through a combination of mathematics and magic. There were, of course, the Christians, for whom the world is simply a preparation for the better life that is to come.
As said, relating what people think to what is happening around them is not easy. But the last few centuries of the ancient world were ages of great uncertainty. There were epidemic diseases that swept away multitudes without warning and without apparent cause. There were barbarian raids and civil wars. There was catastrophically overextended government to grind the survivors into helplessness and poverty. In this sort of world, teachings of Epicurus about seeking happiness in this life may have lost their attraction.
In one of his more sensible comments on Epicurus, Plutarch writes:
As to the vulgar sort… when they lose their children, wives, or friends, they would rather have them be somewhere and still remain, though in misery, than that they should be quite destroyed, dissolved, and reduced to nothing. And they are pleased when they hear it said of a dying person, that he goes away or departs, and such other words as intimate death to be the soul’s remove and not destruction. …. …. And they are discomposed when they hear it said of any one, he is perished, or he is gone or he is no more…. And therefore it is very plain that with the belief of immortality they [the Epicureans] take away the sweetest and greatest hopes the vulgar sort have.
In a world where life is uncertain and often unpleasant, there will tend to be an emphasis on some happier supernatural future.
There may be nothing sinister in the loss of virtually the whole body of Epicurean writings. Perhaps they were destroyed by a triumphant Church that had room for Plato and Aristotle but none for a naturalist enemy of all that Christianity proclaimed. But there is no reason to suppose any deliberate act of destruction. Papyrus rolls were by their nature delicate things. They were also far more expensive and therefore scarce in number than modern books. In any European climate, a papyrus roll would last for about a century, and then the glue that held it together would perish. Without careful recopying, a work might easily be lost.
The last centuries of the ancient world were mostly ages of depression. There was a shortage of all the means that had so far kept libraries together. Such means as remained were naturally given to recopying works for which there was an active demand. That means Christian theology, those parts of the pagan philosophies that could be reconciled to Christianity, and the greatest products of the pagan high culture. Since, with the exception of Lucretius — whose work largely survived — the works of Epicurus and his followers were in a style remarkable only for its plainness, it is unreasonable to suppose that librarians, forced to choose what to copy and what to leave to die, would take up the 37 volumes of On Nature and not the Ecclesiastical History of Eusebius.
So far as I can tell, whatever works of Epicurus survived were not studied in the Byzantine Empire. In the West, all but his name and whatever is said about him in Cicero vanished for a thousand years.
Sean Gabb, “Epicurus: Father of the Enlightenment”, speaking to the 6/20 Club in London, 2007-09-06.