I recently purchased a house that has outside lighting which is plugged into the outside outlets. The GFI that controls these outlets is located in the garage next to the circuit breaker box. After leaving my outside lights on for several minutes or hours the GFI outlet trips. The GFI is 15 amp. Can I simply replace the GFI with a 20 amp to avoid this problem? I know that the GFI is made to trip when there is a ground fault but I can't believe that this would be the issue since it works for sometimes several hours before tripping. Is it that there is too much amperage going through the GFI that causes it to trip. Also, if I were to have an electrician come out to fix this what is the "average" cost to have this repaired.

Thanks!

Either a bad GFCI or you really have a ground falt occurring. GFCI's are not over current divices if too much current was flowing the breaker will trip not the GFCI.

Not sure what it would cost to have a professional fix maybe $100? If the problem is just a bad GFCI you can get a new one for about $15 at your local store. But don't install yourself unless you are confident you know how to do it right.

To directly answer your question, NO!

You cannot protect a 15 amp line with a 20 amp device.

For most home owners, replacing GFI is a quick, cheap test. Replacing can't hurt, 20 Amp GFI can't hurt as well.
I would check recepticles that are protected for dirt, moisture, maybe a lizzard making contact with the hot OR neutral,or any wiring plugged into those outlet(s). If more than 1, unplug a set at a time to determine