When the tentacles are falling apart, the animal is dying. I would recommend removing it as it will turn rapidly to ammonia after it disintegrates. It is difficult to say why without a lot more information. Generally, your water must be as near perfect as possible. Your readings for ammonia, nitrite, nitrate and phosphate should all be 0. If it's a bubble tentacle anemone (BTA) your tank should have been that way for at least 6 months before you added the creature. For any other Anemone, a year is recommended. These creatures love light so you should have strong T5 or MH lighting.
If all those conditions have not been met, you may be able to figure what you did wrong.