I have a neon green BTA anemone that does the same...actually mine barely comes out. I have had him for about 5 months and he's growing and has never moved.

I also have a RBTA and he is out all day long...actually, he mounted his foot on the underside of a large cap and has been slowly killing it over the last few months.

What kind of lighting do you have...tell us more about your system so we can first make sure there's no contributing factors to this behavior.