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Parts for ED25UE - AppliancePartsPros.com

FYI It is not recommended to run a fridge off a GFI line so If possible use another receptacle.
If the unit is on a dedicated line and the GFI is the receptacle type then I would replace it with a standard receptacle. I would check the local electrical code before doing this. Also some houses are wired with a number of receptacles being controlled by one GFI so it is important to know how the wiring is hooked up.

Could be a bad GFI.

Could be a problem with defrost and that is why it takes a while to trip the GFI.
To check this plu the unit in.
The compressor and fans should be running.
Now turn the defrost timer cam (item 6 in section 11). It will only turn in one direction and there is usually a hole in the cover to let you do this without disassembling anything.
If the GFI then trips that is the most likely cause.
Unplug the unit and remove the rear cover in the freezer so you can get to the evaporator coils.
Check the defrost heater.
Check for moisture/ice/frost around any of the connections.
Defrost and dry the coils and connections with a hair dryer.

This may be a difficult problem to repair.

FYI: Since it take very little current (milli amps) to leak from the power side of the line to the frame to trip the GFI any moisture will that gets into a connection can do what you describe.