A simplified version:
Once an attack reduces you to zero hit points (or would reduce you below zero hit points), your hit point total becomes zero. Each round, you must make a Fortitude save to stabilize. The DC to stabilize is 10, +1 per 2 points of damage dealt beyond what was necessary to bring you to zero hit points. If you succeed, you stabilize and are at no further risk of bleeding out and dying.
If you fail, you "bleed out", and lose a number of points of Constitution equal to the amount which you failed the Fortitude save by.
Under this system, "non-lethal" attacks do not force a character to make a Fortitude save upon being dropped: the character is simply unconscious and suffers no risk from "bleeding out".
The Heal skill can still stabilize a dying character as normal, and 1 point of magical healing is still sufficient to stabilize a dying character. Such a character is no longer at risk of "bleeding out" for Constitution loss.
This system has the added bonus of leaving characters who had a near-death experience weakened, adding a bit of "grittiness" to recovery from injury, and further distinguishing between magical healing that works on the battlefield (cure x wounds) and magical healing that is needed for convalescence (to restore constitution damage). It also leaves the door open for weakened characters to be susceptible to disease and infection if the DM likes that sort of grittiness.
...
Of course, given the option, I'd be happiest with a damage save mechanic, but this has served me well when playing D&D.