Scuito my betta was doing the same thing when the water was too cold. I ended up putting a small space heater near his tank and used that to try to keep the water at a consistant temp. He did eat more and was more active. (That was a couple of weeks ago). He is in a 10 gal tank now and the water is at 78 with some Corys, but I think he has other issues as he is getting very white around the mid-section of his body and not eating.
Good luck with your betta.