Although I don't mind what you are suggesting, it only solves 1 instance of your problem. Play this game long enough and you will lose downed party members for all kinds of stupid reasons. The real solution is the game shouldn't kick out of turn-based mode while any party member is down.
Certainly better solution ...
Combat should be hold untill all members of team are at least alive. :-/
And if anyone of them step in fire with last HP during conversation and die, or simply die of damage over time ... they should automaticly sucess on those saving throws. :-/
(happened to me once luckily it was one of conversations where you actualy can swich characters and use help)