Usage/Resource dice mechanic: An opinion and a question

Usage dice from The Black Hack or the Resource dice from Forbidden Lands is a mechanic where instead of keepick track of the exact amounts, the amount of your resources is abtracted through the use of dice (between d12 and d4). After using a resource, you roll a die and if the result is 1 or 2, your resources are spent and the die drops to the next lower die (f.e. from d10 to d8). It works vice versa when gaining a resource. When you roll 1 or 2 on a 1d4, you are out of resources.

Now to be honest, I only the mechanic in theory and it seems simple enough. I like the concept and feel like it can be even used to embrace a narrative. For example you had 3 unlucky rolls in a row and suddenly find yourself without food way sooner than expected. But instead of just treating it as a sudden decrease in numbers, you turn it into a story: "The chunk of meat you bought is actually inedible, the shopkeeper swindled you." or "Insects have infested your rations and now aggressively seek another food source, you." etc.

It fits the design I am aiming for and mixes up well with other mechanics I use. But here's the question: How is this mechanic used over time? For example during longer periods of travel? Let's say the party has to eat at least once a day, so once they are camping, all players roll their die to see if their resource if spend. But what if they travel for 7 days? Do they roll at the end of the travel period for each day (so 7 times)? This is the one thing I currently can't wrap my head around and maybe the solution is actually simple.