I do think this is a serious weakness in the WFRP3 system - it's very hard to suspend disbelief when the GM is putting up ropey "narrative" arguments why something that took 5 seconds in the middle of a fight takes 30 minutes when everyone is chilling out (i.e. fatigue recovers quickly when you're running around!)
I've been thinking about this a lot, and here's my solution. And it also works for healing miracles and anything of that sort. However, it requires a bit of extra book keeping and having never tested it, I'm not 100% sure it works!
1) Keep track of Wounds, Fatigue and Stress picked up in encounter mode as usual.
2) Any cards that heal or remove only do so temporarily. So, when you get an effect that says "heal", simply take the counters / wound cards and put them somewhere else for safe keeping.
3) When encounter mode ends, the adrenalin fades, and those wounds, fatigue and stress come flooding back. You then have the option of using the very same talents, miracles and actions once more for a permanent effect, but because you're in story mode you're back to "once every so often".
There's still a fair amount of narrativium involved in thise, but at least the contrast isn't so stark. And I'll confess, I originally came up with this concept for Healing miracles (Healing prayers in combat are temporary, Healing rituals in story mode are permanent), and hadn't thought of applying it to Fatigue or Stress. But it should still work, in theory.
Downside, players might immediately pass out from accumulated fatigue at the end of a fight. But do you know what, maybe that's actually realistic (thinking of people fainting moments after crossing the finishing line of a marathon for example)