A short rest is "one or more hours." Technically, nothing is stopping the characters from doing that except the DM. Mike Mearls even mentioned that in a video before the Starter Set was released. A couple of points though: Our DM simply stated you are taking a short - there was no discussion of hours, or stacking short rests. It was either one short rest or a long one - problem solved at our table. The second point, there was a lot of Hit Dice recovery at second level (where we all had two hit dice), where a 1 was rolled on one dice, and a 2 or 3 on the second. That meant that a character with 20 total hit points who was down 10 or more was only recovering 3 or 4 by burning all his hit dice on a Short Rest.
Did you add your con modifier to each hit die rolled?