I don't stop counting rounds (therefore the encounter isn't over, therefore there are no short rests for you!) until a dying character is either stabilized, or has shuffled off the mortal/semi-mortal coil.
I'm not 100% sure this is in sync with the rules, but it's how we've played since day 1.
This is how I play it and having listened to the PVP POdcasts w/ Chris Perkins as DM, this is how he plays it too.
After one encounter a player was down and still making Death Saves, they were going to take a short rest and one of the players said he was needed to be healed since he was dieing. One of the other players asked something like, "But were done fighting, doesn't he just pop up?" to which the response was a resounding "No!"
Once they have stabilized, they can spend what they want on healing Surges.