By classical civilization, I mean one that form the ethical, governmental, scientific, or lexical foundation for cultures that follow. Such a civilization's impact lasts for centuries if not millennia. There are many examples of these civilizations in our own history. The most obvious examples are the Greek and Roman civilizations which have impacted Western civilizations in countless ways (the words ethical, governmental, scientific and lexical all have Greek/Latin roots). Another example I have in mind is Confucianism, which impacted the sociopolitical systems of many East Asian cultures. On the other side of things, there are have been countless civilizations who have been overshadowed by more influential cultures. Think about the Celts in Northern Europe. Though parts of their culture survived, they were largely Romanised and have little effect on today's society.
But enough history, this is about worldbuilding after all.
For my setting, I am creating several ancient cultures who flourished roughly 500-1000 years prior to the story. I want at least one of these to be a foundation for a neoclassical revival. Why would an ancient civilization be "targeted" by such a movement? Or more to the point, why would one ancient culture overshadow another? This is not to say the civilizations not chosen are completely forgotten or irrelevant. The ancient Babylonians had quite the influence on the more prominent Greek sciences, for example. I'm just looking for some rationale why a certain civilization's influence would be prevalent centuries after that civilization's decline.