Scabbing and redness across the back is a really important sign of allergy to flea saliva. This can come on even in adult cats and even 1 flea can set it off- it may or may not be itchy. You will probably never see a flea. A very sensitive test you can do at home is the wet Paper Test (see below)
I would be very suspicious of Flea Allergic Dermatitis (FAD). Before you do anything else you should treat all your animals with a safe effective product like Frontline, and hoover and treat your house. More info on fighting fleas:
http://www.fabcats.org/owners/fleas/info.html
An allergic cat needs to be in a scruplously clean environment
If this does not improve the problem, then she could be suffering from miliary dermatitis or eosinophillic granuloma complex. This needs to be diagnosed and treated by a vet. More info:
http://www.fabcats.org/owners/fleas/itchy_cat.html
However these conditions are usually quite itchy.
So I would advise your flea hygiene is absolutely tip top (more so than with a normal cat) to establish at home whether your cat has FAD. If there's no improvement then you should see a vet.
John
The Wet Paper Test:
1. Comb your pet's coat vigorously
2. Collect any debris from the comb onto a piece of white, wet paper.
3. Leave aside for a few minutes.
4. If flea dirt is present you will see black particles surrounded by a rusty red pigment.
5. The red pigment is your pet's blood which has been swallowed by the flea. If you see this it means that your pet has fleas.
Vet 8 years qualified from Cambridge University. Experience in medical and surgical problems. By law I cannot diagnose your pet's problem online. You should take your pet to a vet if you are concerned.