If I stop a minoxidil treatment for periods of 2-3 weeks every couple of years, does it affect the results?

It's a great point. Certainly studies have shown minoxidil is toxic to cats and I've included those references below. Stopping minoxidil for 2 weeks is unlikely to be a major problem - check to see how much shedding you develop about 5-8 weeks after your visit. If you get a lot of shedding, then stopping the minoxidil did have a significant effect. But for the most part, it should not be a major problem in your overall treatment planREFERENCEDeClementi C et al. Suspected toxicosis after topical administration of minoxidil in 2 cats. Journal of Veterinary Emergency and Critical Care. Vol 14, Issue 4, 287-292. 2004

It's a bad idea to stop the minoxidil. You may see some acute hair loss. Unless the cat gets ahold of the actual Rogaine, I do not see how that would be a problem.

According to research, stopping minoxidil for more than two weeks can be a problem in the meaning that there is no effect in the hair loss. However, if you start again the minoxidil and use this regularly, I don't consider this will be a severe issue.