It would be interesting to know what kind of mice they are. The wood mice here just take very small amounts in between the neighbourhood cats and the tawny owls doing their rounds. They tend to try and hide the food with stones and leaves in the food bowl rather than stash it elsewhere, probably a bit too dangerous with all the predators around.
Never thought that I would say this, but it sounds like you need a cat…only joking! 🙂