While there are a lot of questions concerning how to give players fewer resources (usually by reducing the frequency of rests), this question is the inverse: I've had issues at my table with the infrequency of short rests affecting class balance and encounter balancing.
At my table, most "adventuring days" will conclude without a single short rest. The primary reason for why short rests are so uncommon is because both myself (the DM) and my players find value in maintaining a somewhat plausible/immersive narrative, and short rests feel like they break that. It simply doesn't feel appropriate for adventurers to break for an hour after loudly slaying a room full of monsters while dozens more prowl the same dungeon. What's to keep those monsters from jumping the players while they rest or laying an inescapable ambush? As a result, the players don't often take short rests, and I find myself hesitant to encourage them to take short rests in order to avoid narrative inconsistency.
This produces a number of issues, most of them relating to class balance and spotlight issues. Classes based around short rests, like monks and warlocks, tend to feel extremely resource-poor in comparison to classes based around long rests, like wizards and clerics. 5e expects short rest classes to have higher resource availability, however, if short rests never happen, they end up simply having fewer tools to play with in comparison. This is obviously frustrating for players of those classes.
Moreover, my table mostly runs pre-built modules published by Wizards of the Coasts, where the encounter design in those books (in my estimation) seems to expect a party with full resources for each fight. Combat can be incredibly lethal if half the party has no resources remaining, and I often find myself needing to artificially "soften" encounters to avoid TPKs.
How can I allow my players to take more rests without breaking immersion? I want to restore class and encounter balance without creating a scenario that challenges the table's suspension of disbelief.
Direct solutions based on personal experience are preferred. Or maybe the way my table views short rests is incorrect or somehow twisted, in which case I welcome a frame challenge.
Best Answer
Simplest solution: Switch from 5E short rests (an hour each, too long to occur reliably between most encounters) to something closer to 4E short rests (5 minutes, essentially automatic outside of densely packed back-to-back encounters). You don't have to skip straight to 5 minutes, but making it short enough that you'd believably spend that much time on looting, cleaning up, bandaging wounds, fixing small damage to armor and weapons, etc. is entirely reasonable.
The 5E DMG recommends such a solution (along with 1 hour long rests) as a "rest variant" for a more "epic heroism" feel; you don't have to go as far as 5m/1h rests, but perhaps 15m/4h rests gets a balance that achieves the intended outcome (roughly two short rests per adventuring day between long rests).
I'll note: My tables haven't needed this tweak. But that's mostly because our table considers taking an hour long short rest pretty much automatic unless the next encounter is literally on the other side of next door, or we have some strict time constraint preventing it. The 5E default rules work best if you just remember that adventurers are human; they've just engaged in a fight for their lives, they're not usually going to charge straight into another one without a break. Allow your adventurers to be human(oid).