Fins do grow back with the proper treatment. Where the missing fin is, does the area look fuzzy or is it just irritated like an open wound? Either way I would suggest melafix with good aeration and a little bit of aquarium salt.
If the wound is fuzzy I would use methylene blue 1 drop per 2 gallons Along with the Melafix. If the fuzziness doesn't go away in 24 hours do another dose of the Methy blue. I have found that Melafix, although it says it cures fungus it just keeps it stable so that it doesn't get worse.
Is the fish eating? If it isn't, try soaking the food in garlic before you try to feed it. Garlic is an appetite stimulant. Kents marine makes a great garlic product and I have had great results with it.
As always when you treat fish you want to do all of this in a hospital tank.
