So you're either left in an eternal war, or have to completely destroy him. Idiotic. As if he doesn't want to live!
I think this may depend on the personality of the faction you are fighting. I've had a few factions fight until the bitter end. I usually have to be the one to ask for peace and often they won't accept unless you offer them something, even as simple as making them a client state/satrapy. The larger my empire grows, the more I have factions actually asking for peace. In fact, if one of my client states is attacked and I join the war, I always get a peace request from the offending faction that same turn.

I haven't actually given any thought to looking at their personality until I read your post and began to theorize on why our experiences might be different. Now I'll have to keep an eye out and see if "aggressive" factions fight differently then "defensive" ones.