On the player's side, drama between players, shifting interests, and life are some reasons why they stop showing up at an RP. but an RP can survive without it's entire core cast most of the time. I find that genuinely it's an inexperienced/overwhelmed GM who's made a few critical mistakes or has simply given up on their idea. 

I was in an RP that was struggling to get posts. Some of the players left, and the RP went 2 weeks without seeing a post. I was interested, about 3-4 other guys were interested, but the GM pulled the plug because the pace was slower than what he wanted. 

I also witnessed a GM chase away his core users by being extremely critical of their writing style. It wasn't even an advanced RP! Needless to say, the RP didn't last 2 weeks.

A classic example of a GM setting themselves up for early RP death was making an RP that required two writers to work in tandem with each other to get anywhere. Even if you get 10 players, you just need 2 or 3 to leave to end your RP.

That's not to say that it's always the GM's fault, just that they usually have the opportunity to turn things around provided they set up their RP the right way. But I'm going to say the biggest killer for RPs is probably...

Poor communication.