The most reliable parts of the ship are also the dullest parts.
For example, we've seen the hull give out, but even in those cases, it was due to exotic parasites (e.g. 'subatomic bacteria' - erm, say what?), never something like plain old dull metal fatigue.
To be fair, the ship is brand new & top of the line. It wouldn't make much sense for stuff to just be wearing out already
In fact, the only things they routinely have fail are just plot centered. It's gonna be hard to write crises unless once in a while they can't attack (weapons) protect themselves (shields) go anywhere (propulsion & transporters) or are going to lose the ship altogether (warp core)
The only other things we routinely see go haywire are holodecks, which they treat as experimental, & sometimes replicators. Replicators is an interesting one to me, because they always use it as a means to give early warnings that their entire ship is at risk of going haywire.
"Oh noes... My tea order got messed up. That's weird, but not concerning enough to make me think the whole ship is going to pieces, even though it probably will". That's a handy trick. I mean, the environmental systems would be just as suspectable in most those cases, but if that went wacky, we'd all be crapping our pants.
Speaking of which, I figure the waste disposal (bathrooms) must operate on a similar matter/energy transference type system as the replicators & transporters. It would've been fun to just once at least hear about that going haywire in some way.
As difficult as it would've been to produce, I'd have also liked seeing the artificial gravity fail on the show. That it never did makes it the most reliable IMHO.
Or what if when the environmental systems fail, it doesn't effect the air (as it always does) but some other aspect, like the lighting? The ship's lighting must also provide them with a wider wavelength range like a sun, in order to be healthy to them. So if it went wacky, it could give them all sunburns lol