How is your rabbit doing now on the antibiotics and pain medication? Is he eating any better? Has he started eating his pellets now, and is he eating hay any better? Is his poop looking any better?
You mentioned that your rabbit has cavities and was on antibiotics for that. I suspect that's still a problem and this is probably causing the eating issues due to pain and sensitivity while chewing and eating. 3 weeks on antibiotics isn't usually enough for rabbits, especially with a dental infection. Something like that can take months on antibiotics to clear up. So if the dental infection is still there, your rabbit will need to stay on the antibiotic and pain medication for much longer than 7 days.. I had to have my rabbits on a month of the antibiotic azithromycin for a different infection, and it's a much heavier duty antibiotic than trimaxazole.
So you're looking at antibiotics and pain meds being needed for 4-6 weeks minimum. And you may end up needing to change antibiotics. Trimaxazole(trimethoprim/sulfamethoxazole) isn't always the most effective antibiotic in rabbits due to it's short half life. You may need to switch to something like enrofloxacin, chloramphenicol, azithromycin, or an injected antibiotic like penicillin, cephalosporin, etc.
I've had the best luck with clearing up infections in my rabbits with azithromycin, because of it's ability to penetrate deep into the tissue(and bone), and it starts working pretty quickly(days), where some antibiotics it can take a week before noticing any improvement. Though some rabbits can't tolerate it, because it can cause serious digestive upset in rare instances, so should only be used with rabbits that tolerate it well.
Ideally the infected teeth need to be removed at some point. But that has to happen under sedation when your rabbit can handle it. Having your rabbit on the anti inflammatory pain med should be helping if the right dose was prescribed by your vet. Inexperienced vets often prescribe too low of a dose for rabbits. Rabbits need at least 3 times the dose that would be given to dogs. Do you know what dose of the meloxicam your rabbit is getting, and what weight your rabbit is at now?
Medirabbit: dental abscesses
http://www.bio.miami.edu/hare/jawabscess.html