But it's precisely a dead end caused by failing to clear a mechanical hurdle that is the thing I'm talking about.
Talking through a dead end purely within fiction is perfectly acceptable. Good, even--in moderation. I've made very clear here that it's about invoking mechanics where mechanics have no place. Pretty sure I've said some variation of the phrase "why would you invoke mechanics for this" half a dozen times already.
What I'm getting at here is that dead-ends which
(a) only occur because the characters failed to clear a mechanical hurdle
(b) add genuinely nothing to the experience other than "you spent maybe a minute and nothing happened, what now?" and
(c) do nothing to advance toward any kind of (local) conclusion
are something that should be avoided.
If it happens without invoking mechanics, sure, fine, whatever, knock yourself out. That's part of the conversation of play, and that conversation can have all sorts of things in it. Or, if it happens and invokes mechanics, but the result does in fact add something, anything other than "you wasted a little time, now what?", awesome, have at it--whatever was added is, necessarily, new information, or a new avenue of approach, or something which helps keep the game going. Or, if it happens, invokes mechanics, and doesn't add anything, but does inherently push the situation toward some kind of (local) conclusion, any kind of local conclusion, good, bad, weird, whatever, awesome, more power to ya.
But if all that's happening is the PCs are wasting their time and the players are wasting theirs, why on earth are we invoking mechanics for this? Just keep it in the fiction.
In real life I sometimes can't achieve something I could possibly achieve. Taking risks, uncertain outcomes are part of what makes the game enjoyable for me. When my character swings a sword at an enemy I'm not guaranteed a hit then either, why shouldn't they occasionally fail at other tasks? As far as nothing happening, that's not what's occurring either as far as I'm concerned. You're probing the defenses put in place on the house and you just need to try something else. As a GM if I wanted the character to succeed I wouldn't have asked for a roll. I ask for a roll because I want there to be tension, luck and innovative thinking about alternatives.
If that doesn't work for you there are other games out there.