Hi Natalie. Welcome to Purrs.
Am sorry to hear Mitzi has begun to have grooming problems.
It's a tricky one to pin down when this happens, as there can be a number of causes for hair loss in cats. Some are down to stress, and some are down to physical ailments, such as an allergy to something in their environment, such as flea saliva (even when there are no visible signs of fleas, a previous flea problem can leave cats - and dogs - with extremely sensitive skin.
Another cause could be a form of mange, or even hyperesthesia, which can make cats act and react in highly unusual ways to certain stimulus.
Sometimes vets prescribe steroids. I suspect your vet will be feeling their way with this a bit to see what Mitzi responds to. Zylkene is a great idea anyway, and many of Purrs Members swear by it (including me!).
There may be others along later who have encountered this sort of problem too and can throw some more thoughts into the mix.
Saying "Hi" to MItzi and your other cat too.