One of alternate D&D rules with short rest healing states:
A character can't spend any Hit Dice after finishing a
short rest until someone expends one use of a healer's
kit to bandage and treat the character's wounds.
(DMG p.266)
So, make it the same. Party can take multiple short rests. But can heal up only if every character would have healing kit in their inventory. Make those fairly expensive, limited on sale. And also craftable, but with more scarce resources needed.
Above all that. If player still will take too many short rest, without taking long rest - party will simply get exhausted (by the lack of sleep).
As of long rest. Simply make it dependable on food consumption. Much better use of food in game, and player will not be able take long rest too often due to that.
