I don't do travel trailers but I do work on house trailers, which are a bit different than houses and is probably closer to what you have. First is safety- if you're not comfortable with and know how to safely work on live electrical circuits then you need to let somebody who is qualified handle this. Wherever possible ensure the power is off when working on anything electrical; it may need to be live for testing purposes so knowing how to do the work safely is paramount.
The components used in trailers are of low quality and it's very likely to have a bad outlet; replacement is the fix. More likely is that the connections are not on screw terminals like houses do, but are "backstabbed"; ie inserted into holes in the back of the outlet. These connections frequently loosen and go bad. To solve that you switch the wires to the screw terminals that are on the side of the outlet. Note that if one is done this way (including light switches) they all will be this way and it's just a question of time before they all give problems. Since the wire feeding this probably comes from another outlet, a backstab issue there can show up as a problem here so you must swap all backstabbed connections to the screws, not just this one. Backstabbed switches and outlets can be user-replaced with the kind used in house construction; do be sure the wires fo to the same sides as where they were before (white to silver screws, black to copper screws, green or bare wires to ground). Testing these with a meter will often lead to erroneous conclusions; there is often enough connection to read OK on the meter but not enough connection to carry a load so that you must always switch over all backstabbed connections or you can't know for sure that all is well.
You may also have "pierced' connection outlets and switches. These will not have any visible connections but seem to have a jacketed wire running into or through them. With those, there is a snap-on cover on back which presses the wire onto sharp points built into the outlet or switch which provides the connection. Those are only available from a Trailer Supply store; they are not used elsewhere. Snap off the old cover, place the wire in the channel of the new one pressing it firmly onto the pins, then snap the new cover on. Where these are used there is not box like with the other systems so only this type can be used here unless you install boxes. With this system the chances are that you won't have enough wire length to change to boxes and standard components leaving you to either keep the junk or to rewire the whole darn thing.
Also needing notation is that trailers are not inspected like houses, but are certified as correct and safe only when identical or approved replacement parts are used throughout. If you change to anything else not approved by the manufacturer you will lose that certification and void any warranties or insurance and you will also not be able to legally use them as intended. The only house-type components which can be legally swapped are switches and outlets when they are in boxes- nothing else. This rule applies to the whole trailer and all of it's parts. Most people upgrade anyway but you should know what you're getting into when you do that.
Phil
