I am so very sorry that he is so sick, and with no diagnosis.
What is the dosage of the doxy and the dosage of the prednisone? The pred could be preventing the doxy from working correctly. On the tick list, the recommended dose of doxy is much more than most vets use, 10 mg/kg, roughly 5 mg/lb, TWICE a day.
How much does he weigh?
There is always the concern that there is some kind of cancer/hemangioarcoma, but if it's causing these problems, not sure if it would how up on xray, certainly would an abdominal ultrasound.
It almost looks like your vet is treating for infection, and possibly Addison's?