GFI's DO get weak, but you may have a faulty ground connection in that circuit too, which is what a GFI is there to protect against. If you check all the ground wires, they're bare copper in a house circuit, but I've never taken mine apart in the trailer so I don't know if they're the same, and they're secured properly at ALL connections, then try changing the CFI socket. It's not hard, just don't be connected to shore power when you do it. *grin*.
Hi-Lo 1707T - Tire Minder TPMS on Tow Vehicle and Trailer, 300W Solar Battery Charger, Equal-i-zer WDH
2014 F150 Platinum 4x4 3.5L EcoBoost SCrew