That sounds ridiculous, the number one step in my answer is to find a competent vet in your area. If the shots aren't working, their guess of a prognosis is wrong.
It could be a lot of things, but definitely nothing to do with getting her fixed.
There are simple, painless tests they should be completing on your cat to figure out the exact cause of the hair loss, especially progressive hair loss.
It could be something as non-serious as an allergen, to a bacterial infection, to cushings disease, to ringworm (common reason for hair loss, a fungus) - which YOU and your family can get from your cat.
Lice, thyroid problems, fleas, etc. can also cause this, but the most common reasons are bacterial and ringworm. The best thing to do is to have the vet test the cat, and shave off the existing hair. Seriously, find a vet that isn't into charging you for shots of God knows what (hopefully steriods) to treat something they haven't even diagnosed, and find someone that actually cares about getting your animal better.
It could be something as simple as some flea medicine.
Check out the links in my sources for more information - the best way to help your animals is to stay informed and ask LOTS of questions!