What's the temperature of his water? If it's too cold, you'll notice he'll sit around a lot. However, I think when they get bored they become less active too, because I notice if I haven't been walking by my betta's tank for a while he'll sit quietly at the bottom of the tank, and as soon as he sees me he starts swimming again.
They do have their times of rest/sleep too, just like us. <img src="/images/graemlins/smile.gif" alt="" />