Cheap extension cords don't belong outside.
Moisture gets in. A standard indoor extension cord — even if you’re using it outside — isn’t sealed well enough. Rain seeps into the plugs or along the cord jacket, creating a tiny current leakage that trips the GFCI. That’s the GFCI doing its job.
You fix it by using a cord rated for outdoor use — one with a thick, rubberized jacket and molded, watertight plugs. Look for “W-A” or “outdoor” on the label. Also make sure that outdoor receptacle is covered when not in use, and that the cord isn’t lying in a puddle. If the problem persists, the GFCI outlet itself might be old or sensitive.
Not all GFCIs are created equal. Some are more prone to nuisance tripping than others, especially if they’re close to their trip threshold. If the cord is heavy-duty and the connections are dry, swap the outlet. It’s a ten-minute job.
Your extension cord is probably saving you twenty bucks. That’s not where you save.