You know, monkeys jump from a tree to another tree. There are times they will fall from the trees. Often they survive it, but sometimes they die.
In the context:
Paul: "My friend died from the accident, when he just left the hospital. I can't understand why it happened."
Sam: "I am sorry. But you know, there's an old saying: 'Sometimes monkeys die.' It's not a great saying, but it somehow is fitting that."
So it means, even they survived in the past, but unlucky still died in the end. It is actually a bad joke, but at least it might make Paul laughing a bit or feeling a little better.