"When you get back up, you typically have enough hit points to survive another hit, because healing starts from 0. Those negative hit points don't count against you. But your failed death saving throws are a black mark on your character sheet until you take a rest. If you do go down again in the same fight, you could be in trouble."Which clears up a major point of confusion in the comments section of my last post. The fact that your death saves are cumulative until your next opportunity to rest was something I overlooked in the PHB (it was only stated once, and not in too specific of terms). There still remains a question, however... in the RAW do these so-called "death saves" reset after a short rest or after an extended rest?
I'm thinking the game designers intended on them to reset after a short rest; so that the adventure keeps moving forward and things don't get bogged down. However, for a slightly more deadly campaign, a DM might consider that the death saves reset only after an extended rest - thereby making each day a bit more risky.
On a side note: the first of the RPG Blog Carnivals had the topic "Character Death, Ressurection, and The Undead", and in the carnival's closing summary there are links to several previous posts from bloggers discussing the finer points of killing off your player characters.