How's he doing? I think some bettas (or fish in general) may be more sensitive to ammonia than others - kinda like some people are more sensitive to pollutants than others are.
And, according to this site I found, I think it is VERY possible it is ammonia poisoning:
Ammonia Poisoning Red or inflamed gills. Fish are gasping for air at the surface. New tank setup or a tank with too many fish. Ammonia poisoning is easily preventable. Avoid adding expensive and less hardy tropical fish until the aquarium has cycled. For more information on cycling your aquarium please read about the aquarium nitrogen cycle. You can use a substance called zeolite to help absorb ammonia but the best solution is to ensure that your aquarium has cycled and that your tank is not overcrowded. If your tank has not yet completed the nitrogen cycle, you will need to perform frequent water changes to keep the ammonia levels down.
I really, really think he probably needs more frequent water changes and/or a larger living space. If money is tight, go for a Sterlite container.
Hope that helps!