Holy thread necromancy, Batman! (Sorry, I had to say it.

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Okay, here's what I did:
Everyone has a death threshold (DT). Your DT = 0 minus your Con score. For example, Herne has 16 Con; his DT is -16.
At 0 hp, you're disabled (still conscious, can take a single move/standard action). If you get healed above 0 hp, you can act normally, but you're staggered for 1 minute.
At -1 hp, you're unconscious and dying. each round, you make a DC 10 Constitution check; if the result is DC +0 to +4, there's no change. If you succeed by +5 or more, you become stable (0 hit points) but remain unconscious. If the check fails, you lose 1 hit point. Three failures, or a natural 1 on any roll, and the character dies. This roll should be made in secret by the DM so as to keep tension in the game. (Note: This system does not require consecutive saves or failures - as long as you're below 0 hp, you continue to roll until you stablize or accumulate 3 failures.)
If you're stable, you have a 10% chance per hour of regaining consciousness (1 hit point). As above, you're staggered for 1 minute but can act normally otherwise.
If you take damage while dying, it has no effect unless it is greater than your Con score, in which case you must make an immediate DC 15 Con check or die. Even if the check succeeds, you take another step toward death (this could easily result in death anyway for someone on his second step, as a third failed roll means instant death).
All healing applied to a dying person has only half the normal effect, except for the heal spell, which works normally and removes the staggered condition.
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Thus, no one but the DM knows exactly how long the PC has to live (though a Heal check could determine how close he is to death's door). Survivability is based on your health instead of a random chance, and being dropped to bleeding actually has an effect on PCs.