Hi,
Well...there is no such thing as "snuffles". It is a generic term that has come to mean just about any infection or problem a rabbit may have. Most likely it was intended to reflect what we now know as an Upper Respiratory Infection (URI). If any vet makes a serious diagnosis of "snuffles"....I would not consider him/her to be noton top of their game.
Now for your rabbit's concerns. Rabbits can certainly have sensitivities to allergens just as we do. We have one that seems to be allergic to the dust in his hay....and we have also seen him sneeze if his limited pellets are extra dusty. Since the usual response to allergic reactions are anti-histimines (most don't do so well in rabbits since they act as stimulents) or steroids (which will suppress the already delicate immune system)....this leads to some challenges in treating any allergy situations. Since drug protocols may present unacceptable risks, the best treatment for suspected allergies are to isolate the rabbit from these particular irritants. We routinely shake out hay and sift pellets with whatever kitchen implement will sift the dust from the pellets.
True infections should be diagnosed by culture and sensitivity which will identify the specific pathogen and what drug it is sensitive to. Just wondering what antibiotics were being used? If antibioitics didn't clear up the problem, either the drugs were prescribed by guessing and/or assuming a given infection and were ineffectiveor it isn't a true infection. Using drugs like this is why we are having so many problems with resistant bacteria (MRSA in humans is a prime example). This is a result of the over-prescribing of antibiotics by doctors (both animal and human) along with the general public not following thru on the entire course of drugs. Many vets do not culture (either due to client protests over costs or they think they already know what the problem is). And many use drugs such as Baytril or Sulfanomides such as Septra, Bactrim or TMZ....and these drugs are quickly becoming useless due to resistant bacteria. Ido not use these drugs any longer with domestic animals. The most common pathogen found in URIs in rabbits is a bacteria known as Pasteurella Multocida. It is a faculative anaerobic bacteria which means it can live with or without oxygen. It is quite challenging to treat and can never actually be totally eradicated. Currently my drug of choice, based on safety and effectiveness, is Azithromycin (Zithromax). Pasteurella is usually also sensitive to certain Penicillins such as Bicillin (Pen G), Convenia or Chloramphenicol. We have been able to effectively manage all our infections and our rabbits are symptom free.
Since it appears the condition is caused by an environmental issue, I would chart what you are using and see if the sneezing gets better or worse. Would it be possible to move the rabbit inside? Flies can cause some huge problems. If the discharge continues, I would have a vet culture the discharge to see what is in there. And keep in mind that several other issues such as dental or eye problems can also lead to nasal/respiratory issues.
Randy