Yes I've seen that happen. I believe the skill Grim Determination is what counter acts that if it's becoming a big issue -- granted you need to get into the 2nd tier of War to get it.
I'm pretty sure Grim Determination doesn't stop you from dying, it just lets you stay in the fight longer before getting yanked.

"If your gladiator looks to be winning the battle the Enforcer will allow him to continue fighting even if his health is such that normally he would be saved, thus increasing his chances of earning a win."