And BLEEDING TO DEATH.
Now, there are ways to work this so it's sorta believable, mostly involving a "spiritual" definition of hit points, or a big ol' helping of meta-narrative wherein you retroactively decide whether the PC was dying or not based on whether the warlord got to him in time. I used to spend a lot of time on ENWorld propounding the spiritual hit point approach (the meta-narrative solution would absolutely kill immersion for me).
That's how I handle it -- if the Warlord's cry revives the fallen character, then he wasn't actually bleeding to death after all. The wound was more superficial than it looked. Narrating the description only after the results have been determined is a different mindset than older versions of D&D, but I prefer it and find it makes the game a lot more flexible. YMMV. Nothing in the rules states that an unconscious character making death saves is actually bleeding to death... he's simply in danger of dying; the cause of death can be described in whichever way is appropriate to the situation.
If you don't describe the character as bleeding to death when he goes down, then there isn't anything to retroactively "meta-narrate" into something less serious. Sometimes all that other characters see is that the fallen character is bleeding, but when the character is revived, it wasn't major artery that was hit. If the character dies, then it was a major artery and lost too much blood. If a character goes down and isn't visibly bleeding but ends up dying, then he could have died from internal bleeding.
Hit Points in D&D are a very abstract measure of a character's staying power, and have never stood up well to any non-superficial analysis. The way that I play Hit Points is generally that a serious, life-threatening physical injury has only been inflicted if a character has been reduced to 0 Hit Points and is unable to use a healing surge. I admit it's not for everybody.
(...And as I think about it, my proposed solution earlier in the thread wouldn't actually help with this part. Warlords being able to stop people dying with an inspiring word just doesn't work for me no matter how I slice it.)
If the Warlord was able to stop someone from dying with an inspiring word, then that character obviously wasn't as injured as everybody thought.
This isn't entirely unrealistic.
One word: Minions. I have watched a bard kill several minions in rapid succession by yelling insults at them. They had not been touched by any physical attack.
The flavor text of the Vicious Mockery power says that "You unleash a string of insults at your foe, weaving them with bardic magic to send the creature into a blind rage." It inflicts Psychic damage from the Arcane power source. The string of insults could be the words to a spell which inflicts psychic damage upon the foes. Or the minions get whipped up into such a fanatical blind rage that their heads explode. Or if they happen to be standing next to each other, they kill each other. It's a clearly magic effect -- not simply insulting words -- and it inflicts psychic damage.
If a character crouches down over an unconscious foe and spends six seconds sawing on that foe's unprotected throat with a dagger, I don't think it's too much to ask that the foe should die most of the time. Even in combat.
If combat is too hectic for characters to stop and take a breather (a short rest to spend healing surges and regain encounter powers), then they generally don't have the luxury of completely letting their guards down and focusing on slitting a throat. As long as there are opponents who could possibly threaten a character, I think it's reasonable to say that they still need to inflict lethal damage on a helpless character. It's a concession for gameplay reasons, but it doesn't strain my suspension of disbelief too much.
