In my ideal world, short rests would be 5 minutes (or even 1 minute) with no cap.
This would require some rebalancing for warlocks; at a rough cut, chop their spell slots in half and add a restriction that when you cast a spell using a warlock spell slot, its effects end immediately whenever you recover your warlock slots, unless you then expend a slot to keep it going. This in turn would force a rewrite of the hex spell's scaling rules, but hex needed fixing anyway. The warlock spell list would also need to be gone over carefully to prevent abuse of noncombat spells.
If that kind of rebalancing is not on the table, then a 5-minute short rest limited to twice per day would be an acceptable compromise -- it's what I use in my own game right now. I don't see a narrative problem with this*; you can sit down to catch your breath and that'll work to an extent, but eventually your fatigue reaches a level where that's not going to do the job and you have to lie down and sleep.
Still, it's one more thing to track, and it means the short rest no longer serves its 4E purpose of ensuring the PCs start each encounter with some of their abilities recharged.
*Unless by "narrative problem" you mean the general vexingness of spell recovery being tied to resting. Which I don't like, and have never liked, but that ship done sailed a very long time ago.