Sorry to hear about your bunny . It depends really on how well he copes with the dental work/ syringing etc, how old he is, and how serious his teeth problems are.
It's not an uncommon problem in rabbits, sadly. Their teeth continue to grow throughout their life, so if they don't meet precisely they will grow unevenly, so they can end up with painful spikes to the outside and/ or inside of their mouths, which is what causes them to stop eating. To access the teeth, they need a general anaesthetic, so that the teeth can be burred down safely. Often after the dental work, they are still sore for a day or two (although your vet would usually give him painkillers over this period). Some of these guys eventually develop deformities of the jawbone (osteomyelitis) due to the problems with their teeth, and this is unfortunately pretty irreversible.
The main consideration obviously has to be your bunny's quality of life. If he copes reasonably well with the GA/ dental, and comes back to eating in a few days, without dramatic weight loss, or gut motility problems, then there is no problem with repeating the dentals. I have known rabbits who needed intervention every few months. If, however, he is finding it harder and harder to recover, is losing weight and generally unhappy a lot of the time, then euthanasia is a realistic option.
Doing nothing isn't really an option, as when their teeth ARE overgrown they experience a lot of pain, due to the teeth spikes slicing into their tongue and cheeks (I have seen some truly horrible sights ). Rabbits in pain are usually fairly easy to spot- they huddle, often in a corner, don't move much, don't eat, and sometimes make a horrible grinding noise with their teeth. It may be worth airing your concerns with your own vet, as he/ she will have seen your rabbit's teeth and witnessed his recovery period, so could probably make a better guess as to whether or not he is benefitting from the dentals than I can. Don't be frightened to question his treatment- most vets are more than happy to explain the why's and wherefores AND to listen to client's concerns- you DO know your own pet better than anyone. Good luck.