Sounds like they are getting eaten away by fungus or bacteria.
Try looking through these sites for answers:
Answer these Qs to help determine if it is a tank issue (unlikely since only one fish is affected, but better safe than sorry):
~What are your tank parameters (ammonia, nitrites, nitrates, temp)?
~ How large is the tank?
~How many fish are in the tank? What kinds of fish are they and what are there current sizes?
~When is the last time you did a water change and vacuum the gravel? How often do you do this? How much water do you remove at a time?
~How long have you had the fish?
~Have you added anything new to the tank--decor, new dechlor, new substrate, etc.?