Have you checked the wiring in both the plug and the receptacle? Have you checked the grounding of the trailer wires where they are attached to the frame? Sometime under the ring terminals, between the bolt head and frame, you will find corrosion and the resulting poor contact.

If all the wiring is correctly placed, there are no single strands crossing from one pin to another, and you can't find any wiring insulation worn or broken, I would suggest you apply some dielectric grease to the pins of the plugs. Insert and remove the plug several times. If you had any bad contacts caused by a corroded pin or socket, the grease usually restores them to working order.