I had the same problem. Bought aquarium w/yellow polyps. Guy said he never fed them (photosynthetic.) Had for 6 months and they were multiplying. I moved them to a slightly more agitated area of the tank (put a ricordia where they were) and they started dying. Moved them back and they continued to die off. All gone.
A biologist friend bought some 9 months ago. LFS said no need to feed. Soon they started to die off. He went to his books and book said feed them (although they are photosynthetic). He fed them and they are now multiplying.
So, I don't know what to tell you Mr. Bond! They seem to be highly sensitive to position or change of location? Logically, I have to think they would not have tentacles if they don't need fed. Many other marine animals are photosynthetic, but still use other means to acquire sustenance also (corals, clams, anemones, etc.) When I get more I will feed them.
Live long and prosper.
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Glass 90 and 110, skimmer in both 30 gal. sumps, 1150 GPH, plus a 75 gal fuge!! Yellow tang, several damsels, 2 lg flower anems, brown & rose BTA's (8" dia.) with 3 perculas, 5 ricordia, dozens shrooms, dozens of yellow, brown and green polyps, lots of snails, hermits, bugs and 3 inch worms. Mangroves, caulerpa, LR, LS, pics coming