Slade,
It also depends on how your gfci outlet is wired and what other things may be included in that circuit. GFCI plugs have 2 different sets of terminals - one called "line" and one called "load." If there are other plugs that are on the same circuit wired into the "load" side of your gfci then those items (like a refigerator, toaster oven, etc.) must be included in the load calculation and if the total is close to the 15 amp rating of the gfci it will trip just like a circuit breaker would.
Also, if there is more than one gfci device in a single circuit you can have the same problem.
This issue can get a little complex if you are not familiar with house wiring.
Try using a non-gfci plug circuit, if possible. If not, and if you are not comfortable working with electrical issues, you may have to hire an electrician.