Most betta kit tanks from what I've seen are actually fairly small. And sometimes room temperature isn't high enough for a betta. They should be between 77 and 85ish degrees, I think. You might want to invest in a aquarium thermometer so you can check the exact temperature. (; Also, if it's a smaller tank, it should probably be cleaned more than once a week. Once a week is what I'm supposed to be doing for my TEN gallon. So if it's a small betta kit tank, it should probably be every couple days.
I might be wrong, and people can feel free to correct me, but those are my initial thoughts. (: