I wouldn't be so quick to jump on the "spider bite" bandwagon. Spider bites (and in particular, brown recluse spider bites) are often the diagnosis for any necrotic wound that doesn't have another explanation, at least in human patients. Please see the following links for more information on the mis- and over-diagnosis of brown recluse spider bites:
http://www.medscape.com/viewarticle/518429_5 http://dermatology.cdlib.org/...special/recluse.html
http://spiders.ucr.edu/necrotic.html As Vetter (the last link) notes, these types of wounds may be caused by any one of a number of things, including bacterial, viral or fungal infections, Lyme disease, reactions to poisonous plants and vascular disorders.
Vetter also indicates that brown recluse spiders have a reasonably well-established range, illustrated by
this map. If you live outside their natural range, I think brown recluse bite is a highly unlikely cause (and there aren't very many other spiders you could blame this on, either).
I'm sorry, I'm not a doctor or a vet, so I can't give you an explanation, but there are a number of avenues to explore. It could be an antibiotic-resistant staph infection that is becoming more common in humans, or the cause could be viral or fungal, which would also explain why antibiotics don't work.
Is there such a thing as a canine dermatologist? I know there are veterinary specialists in other fields (opthalmology, for example).