I guess it's depending on what's caused it - does the vet know? If the cause is still there (something stuck under eyelid, dry eye, eyelid folded so lashes touching the eye etc) then it won't heal.
I don't know how similar cats eye biology is to bunnies, but one of my bunnies had an ulcer due to a hay seed in the eye, it was quite nasty at first and after a few weeks with fucithalmic it wasn't really healing...so we swapped to ciloxan and it healed within a week.
Another of my bunnies suffers from dry eye and before that was diagnosed it was there for about 8 weeks with my vet desperately trying everything. When this bunny went to see an ophthalmic specialist he put her on dry eye treatment as well as different eye drops and again it cleared up within a fortnight. Corneal cells apparently regenerate quite quickly, within a week or so for surface type ulcers in bunnies, I wouldn't have thought it was hugely different in cats.
The only other thing I would say is that pain relief is important - eye ulcers are supposed to be incredibly painful and will make the animal feel very poorly.
Good luck, hope yours gets under control easily x x