leather corals...

[Delphinus]

Um ... no, star polyps don't usually do this unless they're unhappy. It sounds like a possible stress reaction.

My impulse reaction is to suspect that either something could be picking on them, or something in your water chemistry is off.

Check:

Is something picking on them? What are your tankmates? What are the neighbouring corals? Any neighbouring anemones?

Have you tested your water parameters? What are they? (NH4/NO2/NO3/PO4/pH/Alk) Test everything. And don't beleive a good value, test kits can lie. Get your readings confirmed by a distinct test kit if you can...

How often are you doing water changes?