Are you getting hit by enemies, or are you using certain fiery attacks that drain your HP?
I'm in the same boat, and somehow accidentally added a 99 stack of double combat points preorder item. Ooops.
Yeah, I have this happening to me as well. The character does not die when the health gets to 0 unless the attack was super strong (like a boss attack). If it is the boss attack strong then the character will die but there is no way to revive them since the game thinks they are alive and dead at the same time.