Why GFCI clicks, even when turned off?
I'd wonder if the GFCI is detecting a fault in the wiring coming into the outlet.  The first step is to verify it's the power by unplugging from the metered base.  The next step, for me at least, would be to verify the GFCI in the meter with a simple tester that includes the GFCI button on the side (assuming it's a 110v style plug, not sure if they make them for 220v).

Make sure your extension cords are a high enough gauge to handle that distance for the number of amps you expect to pull, and be sure to replace them if they are showing any wear.

And if all else fails, replace the outlet (taking careful note of which side the wires are feeding the outlet, and which lines may be daisy chained off of the old GFCI so you can rewire it the same way).



Edit: [From your comment on the extension cord.]

Corrosion could have been the problem.  GFCI detects a leak in current, not necessarily going to ground.  So if there is a bad connection due to corrosion, that might appear to be a leak.  Also, realize that most fires are caused by arcing, and so AFCI are becoming common, which will detect more than GFCI.  That may be what's in the RV, and the reason it caught the issue before the base receptacle.

http://en.wikipedia.org/wiki/Arc-fault_circuit_interrupter