As part of my changes to this, I'm making it considerably more accurate.
You will now only receive this warning if a member of the active party is within 4 turns or less of dying at their current regenerate rate. In essence, this means you will see this message far less than you used to.
That said, when you do see it, it means Business.
I picked 4 for a perfectly cromulent reason, if you're curious: If you don't notice until the first warning what your situation is, 4 turns lets you unsummon a guy, summon a healer who can fix it, and gives them a turn to do so. Of course, you only need that for rescuing the summoner: anyone else you can just unsummon.
I still be changing it allow you to take one step/turn when using mouse methods of auto-travel/explore/rest, just like keyboard ones do, so you'll be free to "argue" if you wish, but given the much improved accuracy of the warning, I'd be wary of doing so lightly.