Black scabbing on chin and extends to nose and eye area

My cat has been suffering from black scabs on her face, on and off for the past 6 months. It starts on her chin and it slowly spreads to her nose and eyes. I’ve seen 4 different vets and the treatment has always been antibiotics, they work but it always relapses once the antibiotics stops. We have not been able to determine the underlying cause, we are now trying a hypoallergenic diet because the latest vet suspects an allergy, but her scabs and skin redness are still getting worse. Any advice on how to manage these scabs or a way to find out the underlying cause?

Hello - do they use antibiotic tablets?  This might be feline acne, in which case it may be that it will come off with repeated dilute chlorhexidine washes.  This is helpful because chlorhexidine takes the form of a superficial scub or shampoo and does not involve putting antibiotics into the body.  Like spots in people, feline acne can be more likely in stressed, ill or tired individuals or those with underlying enocrine issues, so a full health-check as well as a diagnostic check of the skin, may be a good idea.  Interestingly, acne can also be associated with a cats' choice of bowl!  Using a ceramic bowl  instead of a plastic one, for example, might help to avoid recurrence in some cases.