Is the only thing you feed him pellets? Bettas like a varied diet of live, frozen, freeze dried, and pelleted food. He is probably just being picky. If I were you I would go to any store that sells fish supplies and buy a container of freeze dried bloodworms, a container of freeze dried shrimp, and if possible a pack of some sort of frozen or live food. I have found that bettas LOVE livebearer fry, and raising them is so easy! Don't buy feeders from the pet store. They are often sickly and really bad for your fish. Instead, raise your own! Platies, Guppies, Mollies, and Swordtails are all livebearers. As for getting uneaten food out of the tank, buy 2 meters of clear plastic tubing from your local hardware store and use it to siphon out the food once a week. I am assuming that you have your fish in a tank, but if you don't: Bettas need at least 1.5 gallons of heated water to thrive, but 3 gallons is way better. If your fish is in a bowl, you should go to walmart and buy a 1 gallon aquarium kit. It is only $10.36 and comes with a hood, a plant, lights for the hood, and an undergravel filter. If you have that tank the water will stay so warm you won't need a heater. Also, your fish will be alot happier, even if it is a little small. If you feel like spending the money, get him a 3 gallon or larger. If you get at least a 5 gallon, he could have a few friends. Feel free to email me if you have any questions about bettas or any other types of fish.
Good Luck!