sometimes they die for "no apparent reason" meaning
they didnt like being shipped to the LFS
they didnt like the way you acclimated them
they dont like your tank
or
they dont like you.
Its really a matter of chance sometimes. All you can do is take the information we know about how to care for them, and give it the best shot.
you do need a larger tank, with Halides (thats my opinion.. I know people say t5 but I prefer the big bad lights),what fixture is over your tank? I didnt know there were T5s small enough for a 6g?
and also, what kind of nem is this?
how big?
what did it look like in the LFS or wherever you got it?
Is it sticky to the touch?
Is its foot planted or is it floating all over?
The more info the better, and if you post a pic, it would be easier for us to help you!
Ive had two RBTAs that disentegrated in my tank (looked awesome the first two days, then keeled over), and now I went the opposite route, bought a sick anemone. that was majorly bleached, and it is recovering and growing like mad! It just really depends on so many factors it is hard to answer the question of "what to do"
Please give some more info!
Good Luck
Jess