Every time a question of "How did X person's writings survive so long?" it sort of begs the question: why didn't others'? The thing to remember is that Platonic and Aristotelian philosophy survived so long primarily because it was popular. Often, we conflate Greek philosophy with just these two men, but the fact is that there was a huge number of philosophers and rhetoricians out there writing; just very few of them have actually survived. Why did Plato and Aristotle? We can primarily thank early Christian theologians like St. Augustine for that, at least in the west, as well as the heavy reliance on Platonic philosophical ideas in the Byzantine Empire (which also likely contributed to their spread to the Muslim world, and through there, back to the West during the Renaissance).

Which is to say, in short, it survived for a long time because it was popular. It only seems impressive in relation to the fact that so many other writers and philosophers from antiquity have been lost to us. This is, in many ways, the same explanation as to why many works from antiquity survived. Why, for example, did the 'Commentarii de Bello Gallico' survive so intact?

What I am getting at here is that it is sort of a self-answering question. Why did Plato survive? Because they did. By the late medieval period when Renaissance philosophers were starting to devour newly re-discovered texts from antiquity, it was that which survived thanks to those earlier focuses from early Christian tastes which they had access to, and thus replicated even further.