Hi there - thanks for getting us started with that great information! I'm Dr. Sara - I'm a licensed veterinarian who works exclusively with dogs and cats.
Round spots of hair loss with crusting like that first strike me as bacterial. This would be especially true if the lesions respond to antibiotic medication. A bacterial skin infection is usually a symptom of either allergic or hormonal disease, and it will often recur after treatment if the primary underlying disease isn't treated. So if we have allergies but we aren't getting any maintenance allergy medication (like Atopica or Apoquel) or allergy shots, the pyoderma (bacterial skin infection) will continue to recur. Allergy testing is only the first step toward sorting out these troubles - once we know what they are allergic to, we formulate a vaccine to desensitize them and dampen future allergic reactions and decrease the frequency and severity of secondary infections. I also mentioned hormonal - both hypothyroidism (low thyroid) and Cushing's syndrome can cause recurrent bacterial skin infections. They are best diagnosed with blood work to check the thyroid, liver, and cortisol levels and function. If we manage the hormonal disease, we can reduce the occurrence of bacterial overgrowths.
By far and away, bacterial pyoderma would be my highest suspicion for any round crusting lesion, however, there are a few others to note. Fungal infections (ringworm) can cause very similar lesions and can be difficult to differentiate from bacterial without some testing. A fungal culture is usually easily performed at any vet's office. Another disease I see that causes round crusting lesions with exudate (pus) under the crusts would be an autoimmune disease like lupus or pemphigus. These diseases are far less common but they can be quite striking and severe. Some are easily controlled with steroids while others are more difficult. These are diagnosed by taking surgical biopsies of the lesions and sending them out to the lab for dermatohistopathology. This may cost hundreds of dollars, but it may need to be done to diagnose the problem. In a financial pinch, some vets will do a trial course of steroids to see if the lesions respond, however, steroids would also treat allergies, so it would be difficult to tell what disease we had - it could still be either.
So if these are really bacterial lesions, your vet should easily be able to put forth a diagnostic plan to check for hormonal issues and an allergy maintenance plan. If they don't look bacterial to the vet, skin biopsies are likely your next step.
I sure hope that all of this information helps - please let me know what other questions I can handle for you.