Hi there!
It does indeed sound like your cat might have lost connection to the food for a period of time. This is usually caused by low script run on a region or other issues affecting scripted items.
It is hard to say what is going on with the hunger without seeing the cat or knowing a bit more information. The main thing to remember is that cats can not eat when they are sleeping. Usually in these situations where users are trying to lower hunger, the cat has fallen asleep, which stops them from eating and their hunger can appear to be stuck and starts to increase after a bit.
Toggling between prim modes is a great way to reconnect the cats to their food. I would also go ahead and re rez the food and also check your region script run. You can check the script run by using Ctrl+Shift+1 and look down the list, you will see script run under Simulator. The higher the script run the better, the goal is to be close to 100% because this shows the % of scripts on the region that get to run each cycle. If the script run is lower that is likely the issue. If the script run is under 50% then you need to for sure request a region restart to help with that, and perhaps have the region owner check into what might be causing the low script run issue.
If you try all the above and are still having issues with your cat eating, please file a support ticket and include the cat ID# and the location of the cat and I will be more than happy to come check things out and see if we can figure out and resolve the issue