It would make sense and the capture harder, if the pokemon just ran away at some point.
Some Pokemon do run away. I'm not saying that. I'm saying that as a matter of honor, a good trainer would know that if they caught a Pokemon while it was unconscious the Pokemon would hate them and never obey them and they need to win the Pokemon over first. So when it's fainted, it isn't running but the trainer as a good trainer won't try to capture it.