Sounds like you are you fragging the corals from your own tank and placing the frags back in the main tank, right? Are the mother corals doing the same thing or are they 100% healthy yet? I've had this happen to the base of new softies i've aquired at an LFS but not from frags of my own healthy mother corals. I think it can be a bacterial problem and it can be spread from coral to coral(at least in my experience it was). I have done iodine dips in the past, but don't recall how effective it was in solving the problem, sorry. also, put them in a low current.
You may also want to try a different method of fragging with colts. I use 2lb test fishing line (or thread)and needle method (cause they tend to slime alot after they are cut) Just go right through the base of the frag once or twice and tie around a piece of rubble rock. Anyway that what has worked best for me.
