I would dip them too. Check out the zoanthid forum here, they've got some pretty good pics of zoa eating nudis. They kind of look like berghia actually, with the little feathery things.
Dip them in freshwater and then do a saltwater dip with lugols in it, I usually do about a drop per gallon but I think that's overkill.
Have you seen any sundials in your tank? That could be another culprit...usually nudis eat the polyps, not just cause them to close up.