Let It Ride
Nothing can protect players from a GM who doesn’t follow the rules, and that includes LiR. But LiR is supposed to prevent abuse. There are messy cases, of course, where you can argue either way, but you should never have players roll repeatedly until they fail, and they should throw dice at you if you make them.
Your example of Andy sneaking still rubs me the wrong way. If he succeeds at Stealthy, you Let it Ride. That means as long as he’s sneaking there, he succeeds. If he decides to assassinate or loot, you should not call for another Stealthy test. You’ve already established that he’s stealthy! What you can do is decide whether or not his original task and intent cover his new intent. This can also be done for focus. If it’s not central to anything go ahead and let him rob the vault or slaughter everyone like a ninja—but this is as much Say Yes as LiR. If you think there are new obstacles, they can’t be stealth obstacles, so you can call for a different roll. “Sure, you can sneak to the vault, but there’s simply no way to enter stealthily. There’s no cover. You’ll have to rush the guards and try to take them out (Knife or some other appropriate weapon) or do something else.” Or maybe “Sure, you’re in the vault. Stuff-Wise to get the good loot instead of the sacks full of useless old knick-knacks.” Different intent, different task, different skill roll.
If Andy fails, you’ve established that he’s not sneaky enough. It’s not enough for him to try to change his odds—that would be advantage and disadvantage, which he should have thought of for the initial roll. For LiR to stop there usually needs to be a change in intent and task—not sneaking into the same place or for the same reason. I’d let it go if he’s been doing other things, though. With a session or two in between, a different and clever plan, and some arranged advantage eventually it might be okay to try again. The trick here is that he shouldn’t need to—if it’s so important that it happen, don’t prevent his sneaking. Make the consequence of failure something that doesn’t block the plot. Maybe he manages to sneak as much as he wants and gets away but the guards get a clear look at him on his way out. He’s accomplished his goal but now he’s a wanted man! Or he gets away uncaught but takes that aforementioned arrow to the knee—and he can’t go to any physician because the guards will be looking for suspicious knee injuries. Those gives him the results he needs with an interesting complication.
Technically you’re always rolling Stealthy against Observation, but yes, I’m a huge fan of abstracting totally unimportant NPCs, especially in groups, as an Ob. I even do this with some plot-important, stat-unimportant NPCs, although that trick is a minority opinion here. Is it a hard place to sneak in? Ob 4. Really hard? Ob 5. Sneaking up on a peasant gathering? Ob 2. It’s simple.
If you tell players their characters just can’t do things because you don’t want them to, you’re doing a disservice as a GM regardless of the game. With BW you have the added concern that players often can (and should!) ask for huge results from one die roll. Sometimes the task is impossible and you say no, but sometimes it’s just too zoomed-out and you say no because you want them to break the intents and tasks down into more granular pieces. That’s perfectly fine, but maybe saying no is the wrong approach. You’re saying More Details instead, and that’s good, especially when Beliefs are on the line.
One roll to achieve your goals is boring. Ten rolls might be a session. A thousand rolls is an epic campaign. Match the level of requirement with the tone and scope of the goals/beliefs and the game!