My starting point in response to this: what does need to go back to civilisation mean?
Of course I know what it means in the fiction; but what does it mean at the table, for the play of the game?
Does it mean conceding a loss? This is the 13th Age and Moldvay Basic approach: you leave "civilisation" with a finite pool of resources (spells, hps, gear) and you go on your adventure, and if you can't win your adventure with that pool of resources then you have lost, and have to go back to recover resources with your tail between your legs. (Moldvay Basic is a bit less up-front about this and leaves it as an implication; 13th Age just comes right out and says it.)
Does it mean waiting for the GM to tell you that civilisation is available? This is largely how I approached things in my 4e play: as GM I regulated the pacing of extended rests by regulating the availability of resting places. There were a few points of player input: skill challenge successes could expedite that availability; player choices could push things to "just one more fight" within a given pool of resources; and - at higher levels - a player decision to spend resources on a Hallowed Temple could make civilisation immediately available to them. But the notions of win and loss were not really apposite, except on the margins: the players knew that I was framing challenges having a pretty keen eye on their available resources. What was mostly going on here was pacing. Even when the players were making the call, it was largely about their sense of how much more do we feel like proving the point that we can go on on the smell of an oily rag? In some cases this can start to bleed into a version of the previous paragraph: if the players decide to call it quits and take a rest, they are giving the GM licence to narrate that the world moves on in some way that is at odds with the players' (and their PCs') desires. Of non-D&D systems, Burning Wheel works quite a bit like this.
Does it mean having to succeed at some sort of ingame challenge? As per my previous paragraphs there were hints of this in some of my 4e play, but only on the margins. A game where it moves from margins to centre seems to me to run the risk of tedium: the point of spending our resources is to get the chance to recover our resources. Maybe some hex-crawling sort of play could be the non-tedious version of this, as there are trade-offs between doing other stuff but keeping enough in reserve to get home. I think it is, as a practical matter, pretty hard to run this sort of game without having it turn into GM decides - at least in the D&D context, where it is the GM who exercises so much control over what the "other stuff" is and hence how resource-draining it will tend to be.
There are probably approaches beyond the three I've outlined, but they're the main ones I thought of. Once one of them is settled on, we can then start talking about whether and how to flavour things in terms of ingame time periods. Moldvay Basic uses "the day" as its time frame, because the adventure is a spelunking expedition. But as every GM of mid-to-upper level D&D knows, this will tend to break down in the third paragraph approach because spells on a daily recovery make a mockery of realistically-framed exploration challenges. So if the game is going to involve adventures/challenges that unfold over longer time periods than a spelunking expedition, tying recovery to ingame time periods doesn't seem worth worrying about too much, at least until we know what else we want to do with those time periods. Eg maybe if we want the GM to really be able to go to town in the event of taking a rest = concdeding a loss, we want to make those rest periods weeks or even months so the GM can really mix things up without the fiction seeming too contrived. Burning Wheel heads in this direction.
To start with the last paragraph: my own view is that once we look at this through the lens of actual game play it makes very little sense for magic - which is just an in-fiction label applied to a certain set of player resources - to be a device for freely circumventing whatever we think the recovery rules should be. This is one thing 4e got right: eg even at high levels, the players using Hallowed Temple to force a long rest requires non-negligible resource expenditure. (At least that is how it was experienced in our game.)
As far as the relationship between recovery and story goes, I think the real question is what are players expected to achieve on a given set of resources? "Story" then needs to be built around that. If the GM is largely in control of pacing, s/he introduces the story elements in a way that allows resource recovery to take place when necessary (Tom Bombadil, The Prancing Pony, Rivendell, Lorien, Edoras, Minas Tirith, etc). If the game is more challenge-focused, the story elements need to be set up so it is at least feasible for the players to win on a given resource set, and if they lose then it is fair to chalk up a "campaign loss" (as 13th Age calls it).
Whether the ingame time period of recovery then gets narrated as hours or days or weeks or months seems a matter of detail, depending on the other details of the particular story being told. If it's LotR, days and even weeks are fine. If it's Die Hard, then we're talking hours at most.