I'd get a second opinion if it were me.

Assuming it is a Pyoderma; you've mentioned the prednisone, but did not mentioned anything about antibiotics, medicated shampoos, having a culture and sensitivity done from skin scrapings, or ruling out allergies. It's not good to keep an animal on predisone all the time unless is the last and/or only option.


http://www.merckvetmanual.com/mvm/in...m/bc/70900.htm

Primary pyoderma occurs in otherwise healthy animals, without an identifiable predisposing cause, resolves completely with appropriate antibiotics, and is usually due to Staphylococcus intermedius or other staphylococci.

Treatment:
The primary treatment of superficial pyoderma is with appropriate antibiotics for ≥21 and preferably 30 days. All clinical lesions (except for complete regrowth of alopecic areas and resolution of hyperpigmented areas) should be resolved for at least 7 days before antibiotics are discontinued. Chronic, recurrent, or deep pyodermas typically require 8-12 wk or longer to resolve completely.

First-time bacterial pyoderma can be treated with empiric antibiotic therapy such as lincomycin, clindamycin, erythromycin, trimethoprim-sulfamethoxazole, trimethoprim-sulfadiazine, chloramphenicol, cephalosporins, amoxicillin trihydrate-clavulanic acid, or ormetoprim-sulfadimethoxine.
Amoxicillin, penicillin, and tetracyline are inappropriate choices for treating superficial or deep pyodermas because they are ineffective in 90% of these cases. Fluoroquinolones should not be used for empiric therapy. Severe deep pyoderma, recurrent pyoderma, or first-time bacterial pyodermas that do not respond to therapy should be treated based on culture and sensitivity.

Topical antibiotics may be helpful in focal superficial pyoderma. A 2% mupiricin ointment penetrates skin well and is helpful in deep pyoderma, is not systemically absorbed, has no known contact sensitization, and is not used as a systemic antibiotic that would increase the likelihood of cross-resistance. It is not very effective against gram-negative bacteria. This ointment should not be used in cats with any known or suspected history of renal disease because the preparation contains propylene glycol. Neomycin is more likely to cause a contact allergy than other topicals and has variable efficacy against gram-negative bacteria. Bacitracin and polymyxin B are more effective against gram-negative bacteria than other topical antibiotics but are inactivated in purulent exudates.

Attention to grooming is often overlooked in the treatment of both superficial and deep pyoderma. The hair coat should be clipped in patients with deep pyoderma and a professional grooming is recommended in medium- to longhaired dogs with generalized superficial pyoderma. This will remove excessive hair that can trap debris and bacteria and will facilitate grooming. Longhaired cats usually benefit most from having the hair coat clipped.
Dogs with superficial pyoderma should be bathed 2-3 times/wk during the first 2 wk of therapy and then 1-2 times until the infection has resolved. Dogs with deep pyoderma may require daily hydrotherapy. Medicated shampoos should be prediluted 1:2 to 1:4 prior to application to facilitate lathering, dispersal, and rinsing. Appropriate antibacterial shampoos include benzoyl peroxide, chlorhexidine, chlorhexidine-ketoconazole, ethyl lactate, and triclosan. Shampooing will remove bacteria, crusts, and scales, as well as reduce the pruritus, odor, and oiliness associated with the pyoderma. Clinical improvement in superficial pyodermas may not be evident for a least 14-21 days, and recovery may not be as rapid as expected.


http://inpractice.bvapublications.co...tract/25/7/418

PYODERMA - bacterial skin infection - is one of the most frequently seen conditions in small animal practice and yet also one of the most frustrating to treat. Around 90 per cent of pyoderma cases in dogs are associated with Staphylococcus species. These bacteria are not especially virulent and infection tends to develop secondarily to an underlying cutaneous, metabolic or immunological abnormality. Allergic, keratinisation and follicular disorders are the most common skin diseases to trigger infection.


http://www.jaaha.org/cgi/content/abstract/33/4/355

Twelve German shepherd dogs, each diagnosed as having a recurrent or refractory deep pyoderma (i.e., German shepherd dog pyoderma [GSP]), were evaluated for several parameters over a six-year period. Results indicated that GSP could be associated with flea allergy dermatitis, atopic dermatitis, food allergy, cell-mediated immunodeficiency, or hypothyroidism, or could be an idiopathic disease. The combination of diseases present for a given dog varied from case to case. Adequate control of the pyoderma was achieved only after each identified underlying disease was treated specifically, along with aggressive concurrent medical therapy using systemic antibiotics and medicated baths.


Just so you know staph infections are transmittable to humans!