If you don't feel comfortable doing this then don't because it could kill ya. Totally un-power the camper.
Now, if you don't want to spend a few bucks on a new outlet in this experiment then simply remove it. Keeps all wires separate & labeled (for reassembly) and then re-power the camper. Use meter to again test the bare wires for power.
If you now have power there then that confirms outlet is bad. If still no power then look for wiring problem.
I would definitely start the way Wrascal is suggesting. If you have power going to the receptacle, the fix is easy, replace it. Before you do this, do what somebody else suggested, turn the circuit breakers (C
off and back on.
If none of this works, you need to do a bit more trouble shooting. In addition to GFCIs going bad, I've had circuit breakers go belly up. To check the breaker, disconnect the trailer from the house, open up the circuit breaker box so you can access the back. First see if the connections at the CB are secure and do a tug test on any wires in wire nuts. Reconnect the trailer and carefully use a voltmeter to check the wire or buss bar going to the breaker, as well as the one coming out. You can also do this with the trailer power disconnected by using an ammeter or continuity checker across both CB poles. Cycle the CB on and off and see what happens.
If this checks OK it's time to check the wire itself. Disconnect the trailer. Disconnect the wire from the CB, buss bar and the outlet. At either end, check each one of the three wires (hot, neutral, ground) for continuity to ground. Only the ground wire should have continuity if you left it connected. If the hot or neutral have continuity, you have a short to ground somewhere (make sure that the neutral is disconnected at the CB box). Next, check the continuity between each wire: neutral/hot, ground/hot, neutral/ground. If you get any, then you have a short between the two wires. Finally, temporarily connect two wires at a time at one end. Check the continuity between these wires at the other end. Do this with the three combinations. If you find that there is no continuity, you have a broken wire or a wire disconnected at an intermediate junction box.