Well your voltage is high enough. I only worry when my voltage is below 108 volts, and will still run my A/C then.
Next thing to check is under the roof cover. It is a possible bad run capacitor.

Picture on the left is a bad capacitor, the one on the right looks normal.
If you have a amp meter with a capacitance tester, you can remove the two wires going to the capacitor, then test it. But if you do not have one, it is cheaper to replace it, than buy a tester.
Lowes sells a $40 clamp on volt - amp - ohm meter with capacitance, and temperature probe as well. It can clamp over one wire going to a AC motor and tell you how many amps that motor is consuming.
Your run capacitor probably is in the 35 Mfd - 45 mfd size range. I keep a bunch of them on my service truck, and have installed about 8 of them in the past 2 weeks.
Good luck, and hope it starts working right - soon!
Also while you have the rooftop cover off, check the cooling coils. See if they need to be washed. Take a garden hose to the outdoor coil, if it needs it. Just like washing the radiator on your truck, wash it, then put back the exterior cover. It should be washed about every other year, if you use the RV in-frequently.
And you might also want to remove the inside cover, clean the air filter in there, as well as tighten the clamping bolts that hold the inside frame to the underside of the Air Conditioner. This will clamp down on the A/C gasket, and keep it from leaking in rain water. This service needs to be done about every 3-5 years. Do NOT crank down on the bolts, just give them a snug tightness with a nut driver or socket. About 20 inch pounds of torque, or not much!
Have fun camping!
Fred.