How is the output of the blower through the evaporator, if the blow AKA throw from the vents is low it indicates that the evaporator coil is choked (dirt) and thus freezing up disengaging the compressor.
In the above case you need to get evaporator cleaned (serviced).
Another probable reason is low refrigerant charge causing the low side pressure to drop below 20psi engaging the L.P cutoff and then engaging once the pressure increases to 40psi gradually. This is also called short cycling.
In this case you need to top up the refrigerant.
One more reason but unlikely in this scenario is that the condenser is blocked or its fan is not up to the mark causing head pressure to raise beyond 300psi activating the H.P cutoff.
In this case also you need to service the condenser and fix it fan.
