Now now, frustrated as I may be by the ludicrous demands of some to give an irrelevant country flavor that should go to other tags, it was possible that Byzantium could survive in some form past 1500. Specifically, if the Catholics somehow managed a successful version of Varna before the Ottoman conquest (which could have been delayed for various reasons), then it's possible/likely that Byzantium would hang on for a while longer as a dependency of whoever kicked the Ottomans out of Europe.
Unlikely, granted, but not impossible, especially if a player is in charge of one of the Catholics. Having Byzantium as a natural target of the Ottomans is more than enough to represent why they died so early in the game's timeframe.