You seem to have progressed very far into the game, so you should be able to heal sick villagers. Your old ones will die, but that's to be expected. You shouldn't have to start over, just find the reason that your villagers are not doing well and focus on correcting that.

If you want to back up your game, just pause it, perform a HotSync, and copy the game out of your Palm backup folder to some safe folder on your PC. If you don't know how to do that, send me a private message and I'll walk you through it.