I handle it by saying that all the keys words are always true. If you might have a food shortage, then you ALWAYS have a food storage, but JUST BARELY you're making do for now if you pass. So like, all of the things that can go wrong in the hard-hold are constantly in a state of wrongness. If someone misses a roll, then whatever that shortage is, just left some people, or a lot of people desperate.
Example. If you've got a hardhold and the shortage is food. Maybe the place relies on a shipment of food that is extorted from the surrounding farms and that gets the poorest of your people by. Or maybe there is some type of processing that can treat the meats of the animals you hunt and kill but'll poison you without it. Either way, when push comes to shove, You're always describing the people on edge.
Then the move gets missed for the week. Something goes wrong, maybe a truck didn't show up with the food, was held up, robbed, or just late. Maybe the machinery broke down that was handling the processing, and now food that was there suddenly takes a dip.
The thing is you've got two parts of the story here. The first part is where everything is scarce, so even when things are good, they're still horrible. So like people don't have stockpiles of food laying around unless being hungry or famine isn't on the list of things that could go wrong. The second part is that anything that goes wrong this session doesn't necessarily need the player's attention. It might be fine next session. The people that the hardholder has working on these things are acting to fix it without instruction. That could also mean a chunk of the guards are out looking for a truck, or the entire scrapper faction is consumed with the task of repairs and looking for parts... You only need to inject the Hardholder himself into this to manage the crisis, not to solve it.
Some sessions cover weeks, other sessions cover hours. It could be really weird if a player just fixed the machinery themselves, ends this session, and then it immediately misses the next move, so it broke down once again... It can also we weird if something like a famine happens one session, and a few hours later the next session says nope never mind we're good. With that in mind, if something TRULY UNFIXABLE goes down, make sure you put the hardhold's leadership in question so the wealth move auto fails until they find some workaround or solution.
But really, the things that go wrong aren't so much for the hardholder to fix, but instead, they are the background to describe what the problems facing the people of the settlement are. So like if people are hungry, maybe they're fighting for food. Maybe crime spikes. Maybe important NPCs that have the money to get food anyway (like players or people with the jingle around town who saved something just in case, or had a connection to something just for them), start getting attacked. Maybe the Hardholder has to keep his engineers alive, because some of the riffraff are trying to kill him.
It is assumed, I think, that people with the risk of going hungry probably aren't eating every day as it is. If the hardholder finds a way to SOLVE (even just for now) the issues, then remove those weaknesses from the holding. At the same time, always be willing to add new custom ones that fit the fiction.
Does that help any?