What is the most likely reason the republicsame of Yugoslavia held together until the fall of communism

This is a little open for interpretation, but I would generally say that the best answer is that Josip Broz Tito was a very powerful leader, who kept the republics and the different groups together.

For example, we can see this from the fact that the first conflict happened in 1981: one year after his death (a protest of Kosovans who demanded autonomy).