Unfortunately, the root of the usual cause of such a condition is environment and nutrition. You seem to think that environment is okay (water quality). I'm not sure of that.
With the proper nutrition, your fish should be fine. Is it getting the right foods? in the right quantities? with fat additives? and vitamin additives?
I would still believe that its environment is suspect. I've kept sailfin tangs, for instance, that you would not recognize as that fish because its fins were all gone, come back to full fins in three months. It takes the optimal kind of nourishment and environment.
I can't help you out much more on environment, it's something you'll have to find. If you want to answer these questions, I can see if I can spot a concern or problem:
How old is your tank? When did it originally cycle?
What kind of system do you have (tank volume, dimensions, bio-filtration method, the equipment you use, any carbon or chemical filtration, etc.).
List all specimens in the tank (fish, inverts, corals, clams, etc.).
Do you use a quarantine tank and procedure?
Foods you use and feeding schedules.
How long have you had this fish?
Do you use any vitamins? any additives? Please list all.
Chemistries – please give actual numbers (Ammonia, Nitrite, Nitrate, Phosphate, Silica, Ca, Alk., and any others you have)
Water parameters – please give actual numbers (pH and your pH range, salinity or sp. gr. & range, temperature range)
Water changes (how much and how often).
List what you added or taken out of your aquarium system (living, decorations, and equipment) during the past 6 weeks.
Maintenance schedule. What have you done lately?
BTW the most value that activated carbon has is this: For the first few days it pulls out mostly organics (thus its reported success at getting rid of yellowing water). After that, it depletes trace elements. Unfortunately, the fishes need some trace elements to remain healthy. So, carbon IMHO should be used very carefully. It's all part of the 'proper environment' issue.
Good luck!
