There are a lot of variables and things that could be causing this, but the long and short of it is that your anemone is most likely dying.
I don't know a lot about carpets, having never had a carpet myself, but there are some basic questions that should be answered before conclusions are jumped to.
First off, pictures are going to be a big help here.
Tank size?
Tank lighting?
Any lighting changes since adding the anemone?
How old are your bulbs?
How old is your tank, how long has it been running?
How much Liverock?
How deep is your sand bed?
Other tank inhabitants? Fish? Inverts? Corals?
Tank parameters?
Any radical changes in the past month? Any temperature highs or lows, any nitrate spikes, any long amount of time with the power supply out?
Feeding, what are you feeding the nem and how often?
Have you treated the tank with any additives since adding the nem?
And any other information that you think might be pertinent to your nem taking a horrible and sudden turn for the worse.