I think one of us might be overlooking something or reading too much into the specifics of the rules glossary. The "Long Rest" is very explicitly defined on page 19/20 of the expert packet immediately after the words "If you still have inspiration when you start a long rest, you lose that inspiration" & there are many abilities that are keyed to long or short rests, but the only place that short rest is defined within the glossary in both playtest packets is within the long rest itself "If a Long Rest is interrupted by combat or by 1 hour of walking, casting Spells, or similar activity, the rest confers no benefit and must be restarted; however, if the rest was at least 1 hour long before the interruption, you gain the benefits of a Short Rest. "In our playtest we have played 5 levels using the new inspiration rules.
Each character is averaging 1 inspiration every two combats or so. The long rest thing is not a big deal, it is almost irrelevant. Sure we have been left with an unused inspiration here and there but they are so common we are usually using them on the next failed check.
The halfling has only played for 2 of those levels but she has not got a single inspiration yet. Other players have had I guess 20 or so in that time.
The Halfling problem aside we have found both of the new versions (20 and 1) of inspiration to be awful. The 1 is worse because it is a reroll mechanic, at least with the first playtest there was some strategy involved in using it.
In short, inspiration melts for a short rest too