I am getting a lot of questions about AC because of that I am going to post some comments I sent out recently that may help some others. If you fell like I am rambling just delete it and sorry for talking your time. That being said I am always available to answer questions whenever I can help.
You said that you turned the thermostat up to turn it off and back down within a minute. That in its self can create a problem because that short period of time does not allow the compressor to equalize. When the AC is running you have a 250 lbs. to 300 lbs. of pressure on the discharge side of the compressor and around 60 lbs. on the inlet side. As you can imagine the motor doesn’t like to start against a 5 or 6 to 1 ratio (it’s like trying to start a car in gear). That’s why the newer systems have a 5-minute time delay built into the system.
That being said if the pressures are equal and the voltage is correct you should not need a Hard Start Cap. I would check to make sure that the voltage is over 110 VAC when the AC is running (Check this at the AC unit in the ceiling). A hard start kit is a bandage for something that not correct with the compressor or the power supply feeding the compressor.
Along those lines a 2000-Watt compressor is probably NOT enough to run a 12,000 or 15,000 btu AC. There are a couple of reasons, 1- most 2000 watt Gens are only rated at 1800-Watt continuous duty (15 Amps 120 VAC). A 12,000 btu. Two, the AC that runs at 12 to 13 amps @ 120 VAC has a momentary start up current of 25 to 30 amps @ 120 VAC or 3000 t0 3600 Watts. Starting a motor is like pushing a car the first 10 feet is really hard but after you get it moving it’s not so bad. An electric motor is the same because the first few revolutions the motor will draw 2 to 2 ½ times the run load amps. That’s why I say the 2000-Watt Gen is really not adequate for a 12 mbtu. or 15 mbtu. AC even though the run load amps are less than what the max amps are on the Gen.
Now as for low voltage as the voltage goes down the amps go up. Work is a combination of volts and amps which = watts or work. Any motor or inductive component will suffer from this; a 10% decrease in voltage creates a 10% increase in amps. That’s what burns stuff up NOT the low voltage but the by-product of low voltage, which is high current (amps). Resistive components do not suffer for this problem only happens with inductive parts like motors & relay coils. But that’s not the end of the problem as the voltage goes down and current goes up the wire it's self heats up because of the high current and when that happens the resistance increase and the voltage drops even more.
So as you can see any voltage under 110 VAC will create problems serious problems, in most case low voltages cause more problems that high voltage because of the high current by-product.
Next NO Cooling after long run time, IF (key word IF) the compressor is still running you probably have a freeze up problem. Indoor coil freeze up, this is only caused by one thing LACK OF AIR FLOW ACROSS THE COIL when its over 75 degrees outside. This can manifest its self in several ways:
*Dirty air filter
*Impacted Evap coil (indoor coil). This is dirt in between the fins
*Dirty Evap coil surface (indoor coil).
*Inadequate ductwork (Not uncommon in an RV). Duct work to small.
Low Freon will not freeze up an Evap coil at normal operating temperatures. That being said if you are low on Freon your compressor will overheat and shut down after 5 to 30 minutes of run time depending on how low it is. THIS IS NOT COMMON and usually results in a burned out compressor in short order.
Now after all of that remember that on a hot day with sun shining in all of your big windows your AC probably will not be able to keep up. If it’s a scorcher keep the shaded drawn on the South side along with the East in the morning West in the afternoon.