Quite to the contrary. They do need special care, especially if you managed to get the bleached out white kind. A healthy sebae should look something like this:

.
This is a female specimen I have had for almost 14 years, so they can be very long-lived. Off hand, I will say that your lighting is insufficient. Your T5s are not the ones people rave about for several reasons:
1) They are not high output (HO) T5 lamps
2) They do not have individual reflectors
Also, you don't have many bulbs, either. If you are looking for more sufficient lighting and you want to go the T5 route, try looking at the fixtures available. I highly recommend Tek and Aquactinics fixtures. Also, the icecap retrofit kits are even better, if you want to go the extra mile (and $).
Another note on anemones, despite what you may read or hear otherwise, is that they
need to be fed and fed well. I recommend a bare minimum of twice per week with some sort of nutritious, whole meat. This includes chopped silversides (with all parts, guts, etc. included), chopped krill (again, everything included), etc. Avoid feeding only meaty sections, like relying on fillets, peeled shrimp, etc. They aren't really nutritious enough in the long term.
What size tank do you have, exactly? Most of the "hosting" anemones reach a minimum of 12" in diameter, with other more popular species reaching 24"+. Hope this helps you out, despite the horrible advice given by one of our local fish stores.