Oh Sue I'm so sorry to hear you have been told this
Sadly, snuffles can be difficult to 'cure' completely and does have a tendency to recur, but there are lots of different antibiotics which can be tried as well as some other things to see if there is a cause (e.g. overgrown tooth roots) so please don't give up yet - and if your vet wants to, I suggest you change vet!
My lovely little Santa has recurrent bouts of snuffles for no apparent reason, but she has been like this since the end of last year. She does need to keep having antibiotics which isn't ideal, but she is well and happy most of the time - she just has a snotty nose and sneezes a bit!
Did your vet ring the Bristol rabbit clinic? They should be able to advise. Has a nasal swab been taken? It could just be that you've been using antibiotics which aren't totally effective against that bacteria - good ones include septrin (given orally), terramycin (injection every 3rd day) and penicillin (can be given up to daily, although it is considered slightly 'riskier' but usually does the job!) Bisolvon is also a product which can be given, if Dobbin has difficulty breathing, it thins the mucus so helps to keep his nose clearer. Things like tear duct flushing, giving antibiotics straight into the nose or by a nebuliser, and head x-rays to check for tooth roots being the cause, are other things which can be considered.
I totally understand why you're upset and it may well be that if Dobbin is going to be a chronic snuffler, you may not have as long with him as with a totally healthy bun, but many snuffly buns go on to live long and happy lives and can go for months or years without a relapse. Big hugs to you and Dobbin xxx