Had a problem like that, and it was locking out on high head found with tattle tale. Condenser motor was amping fine but checked motor at shaft, bearings were causing motor to lock up.Had a lot of play side to side.
If the tattle tails don't work try using manual reset on you high and low pressure safties. Had the same problem one time but with a UPC board, CTI board and ALC controls. Freeze stat was kicking it out, shorted economizer board it would run the power exaust fans with the economizer closed (long history with this unit its full of FM).
I had an odd situation like that but on a Carrier once. Turned out that the compressor contactor coil was pulling high amps because it was heating up. It had half of our shop stumped because all pressures, voltages and amp draws were in spec. We eventually changed the contactor as a " Let's see what this will do" tactic. No problems after that.
i would check the condenser fan motor capacitors, make sure they aren't cutting off due to bad capacitors. if the unit has a UEM board, unitary economizer module, make sure it has no problems in it. (that thing can cause weird things to happen when you are calling for cooling) check superheat, subcool, make sure you are getting enough cool suction gas to keep your compressor from overloading on thermal protection. lp, hp, freezestats. make sure both cfm are running properly, not just the capacitor as mentioned, but also the relay that brings on the second fan motor, and the outdoor temp sensor that sometimes has a plug connecting the wiring to the upc board, it can come loose, or have corrosion.