When the tenticles start to get stringy, there is usually one of two problems. Either you are not feeding it enough, or there is not enough lighting.
I disagree. This can mean many more things than just two. One, is that it's expelling waste, in which it's normal to see an open mouth, deflated tentacles, as well as brown gunk coming out of the central mouth opening. This is usually cause by incorrect feedings. You never stated which species of anemone this is. All anemones will need a different food source, as well as different requirements. I dread the idea of getting another anemone to replace this one, or any other one in the future. Anemones just don't survive in captivity. The only few people I have seen, keep a nice anemone living and thriving for over 3 years, are the ones with the proper tank setup, and the ones who did the proper reaserch and care, and tried to meet the anemones demands. Anemones are araving at our LFS's today bleached, half-dead (already dead in some rare cases), dyed, discolored (Stress), deflated tentacles, non sticky tentacles, as well as a very unhealthy foot. Most people purchase these anemones. I always encurage doing the proper reaserch long before you buy, I can speak with personal experience with this one.
Your other anemone is likely a new addition, correct? I hate to be nagative, but I doubt it will live any longer than 4 months. IMO, and only IMO, I would take the anemone's back. Try to discurage the LFS's from selling them, esspecielly wild cought anemones.
Sorry if I sounded harsh in any way, I wasn't meaning to.
Good luck,
Graham