They can run continuously. They use the refrigeration as a coolant. So, the system needs to be maintained - sufficient refrigerant, condenser coil regularly cleaned, no obstructions to airflow. Also, run capacitor has to have correct capacitance. Important but rarer issue: correct voltage and current.I am here in DFW and the Central A/C is broke!
Question to the guys in this area:- Are the house compressors designed to run 24x7 or they need to be cycled? I mean if the outside temperature goes from minimum of 92 to 109, in theory the compressor will have to run constantly (if it was working to begin with!).