There are two pieces to this discussion. One is actually interesting. One, not so much.
Not So Much
In JAGS the Endurance rules exist for two reasons. The first is to distinguish running from sprinting. Our assessment of the movement rules, early on, was that champion sprinters run the 100-yards very fast--but they run, like, the first 10 yards more slowly than the last 90. This observation is built into the JAGS movement rules (you must move at "run" one Round before you can "sprint"). From that point we decided there had to be some reason you did not /always/ move at Sprint speeds and, therefore, the obvious answer: Endurance was ... well, not discovered (anyone who has done lawn work or attended a PE class has probably run into Endurance)--but let's say "re-discovered."
Even from the start we knew pretty much what we wanted to do with it: not much. Champions, one of our formative go-to games, tracked Endurance for every attack. We charged "one Endurance point a Round" no matter what you did. The game tracks combat in terms of seconds--outside of Sprinting you can go for minutes. Already that's 'out of scope' for game balance.
Even in combat you get like CON Rounds of action before you're sucking wind. Given that most fights last like 2-4 Rounds and even a mega-battle won't usually go 12, it's clearly just not going to be a factor.
That's intentional: we had very, very little interest in making you run out of Endurance during a battle. It's true that it happens in real life (UFC fighters can "gas" and by round 12 most boxers are pretty tired) but in almost no fiction (save, for example, boxing fiction) is it much of a factor.
No: Endurance exists to stop someone with a lower power attack from, like, leveling a mountain range by repeated fire. It exists to explain why you can't carry your buddy across a desert. It exists to put an upper limit on activities and it also helps explain some drowning rules.
Given that this is a small part of the game, we didn't devote a lot of time to it, and in the interest of brevity, we never said "how long you have to rest to get it back."
That's the interesting part.
So the interesting part is looking at how "time passes" in traditional RPG play. I mean, it's not as straight forward as it might look. For one thing, even "real time" sessions aren't necessarily real-time in the game. It's even arguable that you as a player, speaking in character, might not be saying the same things that are coming out of your character's mouth in some hypothetical "RPG-game reality." For example, if you are playing Star Wars, almost no matter what you say "in character," your actual guy isn't speaking English (and if you roar like a Wookie, does anyone think a real Wookie sounds anything like that?).
Time wise, however, there is a very important concept that divorces game-play from the reality around the table--and that's the concept of a "scene" or "encounter." In RPG-play most of the time the action will (ideally) move from one important or interesting segment to another. Sure, there can be false starts, filler, or attention to detail moments of play--but I don't think it's controversial to say that if you consider RPG-play as a series of "scenes" with some connective tissue you won't be too far off the mark of what a well run game will be like.
The concept of a scene is roughly "when interesting things start happening to when they stop." Because heavy action (fighting? Blasting things?) happen in a scene then the idea is that if you can rest then you get the endurance back "by the next scene."
If you can't rest (because of, say, waves of opponents coming at you) then the "scene" isn't over and you're kind of screwed.
So that was the limit of our thinking--although we had not--and have yet to--entirely adopted the "scene" concept. Why not? Well, for one thing it's very meta-gamy and we want that to be kind of optional rather than always a hard and fast rule. For another thing it's hard to determine what a scene is if you're going to look at the edges (can a player drag out a scene by declaring they're interested in the action?)
On the other hand, we could've determined how long you had to rest in order to regain Endurance. Our method for this is to go to Google and do some research. Then we want to simplify what we've learned and try to arrange it into something that plays well.
I haven't done that for recovery but I can tell you from my history of working out (I work with a Personal Trainer four days a week) that "recovery" is not yes-or-no. What happens (to me) when I really bust my ass in the gym is that the next day I am degraded in my ability (both in terms of maximal effort and ability to work hard over time). This means that a realistic assessment would be pretty complex.
That kind of complexity is possibly only interesting in a really deep "fight game" (i.e. the PCs are UFC wannabes who must choose things like training Endurance vs. training Strength or something). I think we'd be into diminishing returns.
I advise that if period of rest is important then you want to say something like: Once you hit the "Tired" zone (END equal to CON) you recover 1 END for 1 minute's rest (the 1-round between fight rounds) and then after that, up to half you recover 1 END up to half your END. Beyond that it's like 10 minutes per END.
If you keep doing this (working to exhaustion and then resting and working again) you will lose 2pts of maximal END each cycle done in a day. Those are recovered with a full day of rest.
Something like that?