What sort of actions are you permitted to take when you are dying? Can you activate powers that might help you make the save? Also, is getting less than a 20 on a death save considered to be "failing the save"? I ask because we had a character who was dying, and got an 18 on the roll. The player then activated her "Heroic Effort" power, which takes "No Action" and grants "+4 to a failed saving throw". Does that work? Also, is there any way you can leverage unspent action points for a bonus to your death saves?
The Death Saving throw is still a saving throw, you only fail if you roll under a 10. Rolling a 20+ is a special exception that allows you to spend a healing surge. Heroic effort can only be used on a failed attack or a failed saving throw. Therefore it could not be used in this situation. (I'd have no problem with a DM allowing it though, it sounds like a cool use to me). Note that it could be used on a roll of 9 or less (a failed saving throw)