I would purchase a flea comb....(small with very tiny teeth)..you can get them very cheaply at a pet store. Comb through the cat's hair (usually around the hind legs....and rear end)...and if you get little black specks you are looking at flea eggs...if the speck is moving, you are looking at a flea. Some pets have alergies to fleas, and start dropping their hair.... I use Advantage cat flea control even though my guys don't go outside and don't have fleas. I get this at the vet's and apply it once a month to the back of their furry little necks. Seems to work. Let us know how this turns out. I would put my money on fleas being the problem........

Good luck!