Karen, this is very basic so if you already know this, please disregard... but... ammonia absorption refrigerators take a very long time to cool; on the order of four to six hours. Once cool, they work very well.
All that happens when you run your fridge on electric is that a heating element gets hot next to an ammonia-cocktail filled tube in the back of the fridge. The ammonia heats up and expands, and then is forced through a very tiny orifice causing it to cool as it re-liquifies and draws heat out of your fridge box. That's an oversimplification, but generally how it works. If your fridge cools using the gas burner, then the ammonia cooling system works fine; it's merely a troubleshooting issue to figure out why the electric heating element isn't working.
The heating elements are very much like a standard lightbulb in that they are seldom intermittent; they are, in most cases either on or off and work or don't work. It's unlikely to be a heating element issue, or a cooling system issue if it's intermittent.
There are a number of things to troubleshoot electrically to determine exactly where the problem lies. First, when you plug the trailer in, and the fridge doesn't work, do the other 110 AC outlets work? If not, the problem could lie in the outlet that the trailer is plugged into, or the pigtail for the trailer, or the circuit breaker/breaker box connections.
If the other outlets do work, then the problem could be the refrigerator
cord, the plug on the cord, the on-off switch on the fridge, or the wall outlet/wiring that the fridge plugs into.
Good luck and please let us know what you figure out!