I am not sure if FTL is the best example here? FTL is slightly unusual because it has a turn-limit, because you always have to move forward, and you might not have enough time left to recover.
By contrast, in Nethack there are basically no mistakes that damn you to limp along and lock you out of winning. Either you die quickly, or you can recover into a winnable position. (Though you might be locked out of certain niceties for a run, you don't need any specific permanently-loseable nicety to win.)
IIRC (it's been a while) the luck component in it is also largely negative, in that bad things can randomly happen to you but (substantial) good random effects are minor and unusual, so you can't even luck your way into enough resources to have a hope of winning, as in something like Nethack where a desperate prayer or drink at a fountain or something might totally turn your game around. If you're more than very slightly behind, the game's not going to hand you enough to salvage your run, period.
I think part of the trouble is the illusion-of-choice map system. In reality, you have to be taking certain routes to do well, by deliberately seeking encounters, et c. The illusion is that you can take an easy route through an area and still be on a path to victory. IMO the maps are kinda pointless in that game, given how the mechanics work, basically just providing an opportunity to fuck up without knowing it, and also permitting the limping-to-the-end-but-long-ago-doomed effect.
I find FTL frustrating because I like some aspects of it but IMO it makes some major mistakes in terms of game mechanics, to a degree that I find it hard to appreciate the things I like (mainly the tactical combat minigame). I get what they were trying to do with the rest of it—the time pressure cutting off options and forcing choices, et c—but it doesn't all come together correctly. Needed one more conceptual pass to make it all fit properly, which is even more frustrating when it's not that complex a game. All that effort to finish it, but fundamental flaws left in place throughout.
One saving grace is that a game of FTL doesn't really last that long. So even if you limp along, you didn't waste that much time.
I never really went into limping mode, though. I usually tried to turn my games around by staying aggressive; but eg burning through my missiles and drones faster when the run goes badly. In some sense, if you have missiles left when you die, you didn't use enough missiles.
There's some strokes of good luck in FTL, like the scrap collector or the long range scanner. But they tend to increase your longer term average, they don't provide an immediate bonus. (Exactly as you say.)