This may sound strange but have you Cleaned the Air Conditioner?
As they run. Most makes (Coleman is a partial exception) Crud builds up on the fan side of the condenser. as this builds up air flow is impeaded. as air flow is impeaded the unit heats up more and more. Pressure in the system increases. The compressor works harder and draws more power.. The CLUE is the "A few minutes".
The solution: remove outer cover (Shroud) and inner cover (on evap) clean the fan side.
On colemans they "SUCK" instead of "Blow" so the crud builds up on the OUTSIDE of the condeser. Remove cover. peal off. replace cover done.