It depends on the market. Flights from DFW (American), MIami (American) and Houston (United, Avianca/TACA) are year-round, with the number increasing in high season. Flights from Atlanta (Delta) and Charlotte (US Air, currently) are usually seasonal, with weekend/Saturday flights only much of the year, and no flights at some times. Flights from Newark (United) vary depending on the time of year, with more flights December through January. Delta's new flights from LA I think are going to be seasonal. Sun Wing, I think it is, has seasonal charter flights from Toronto. But the flight schedules change regularly, certainly from year to year, so you have to check depending on when you are going. The coming merger of American and US Air may change the schedules, as did the merger recently of Continental with United.
Use a meta-search engine like Kayak.com to check for flights from the markets closest to you, at the time you want to go.
There are on average roughly 29,000 total available seats per month from North America (U.S., Mexico and Canada) to Belize, the next to lowest number of flights to any country in Central America. Costa Rica has the most seats, Panama is second, Honduras is third and Guatemala is fourth.