It's a question that most people have not thought about: How would they kill themselves without using any weapon (or anything that could be classified as a weapon)? It would be almost impossible, unless you are some native body expert, but I don't think there were such things a long time ago.
I'm sure people from ancient times got depressed and were possibly willing to kill themselves, but how? The arms are not used (they got no power) and the legs can't reach the head. Any other part of the body wouldn't work.
Starvation is off the list, as I already thought of it.