One of my boxer's had that issue. My vet and I were able to pinpoint it down to the fact that she is allergic to christmas tree flocking!! It was only happening during Christmas, while we had flocked trees! Funny huh? My best advice to you, is to try to pinpoint what he is allergic to??? I know it's hard, but maybe it's something simple like a plant or something. Good Luck!!
Do you have access to a veterinary hospital that provides specialized care in allergies? Most large universities have such animal hospitals and that would probably be your best bet if your regular vet can't nail down a good diagnosis. Right now it sounds like your vet is trying to treat an unknown by throwing both prednisone and antibiotics at the problem - is it really an allergy or a bacterial illness? Has he done any testing?
my Doxie is having the same problem, we have been going thru this for yrs. we have tried everything, it turned into pneumonia twice over a 5 yr. period. we give him 3 meds regularly. he get a benadryl in the a.m and p.m also he get chlor-tabs which he gets at the same time as the benadryl, he also takes cerenia 160mg. that we cut each pill into 8 pieces. he get that 3 days a week and that is what we have been doing. Our 12 yr old doxie is still like chasing around a snotty nose 2 yr old. he plays, eat, everything else about his life is great except We have a snot fest just about everyday. like I said this has been going on for yrs. If anyone out there has an answer out there is cyber land I would greatly appreciate it.I have heard that a natural nasal saline would help. has anyone tried that? if anyone comes up with an answer it would be greatly appreciated!