The Visteon VS16 is a variable displacement compressor. It shouldn't cycle off and on. Evaporator temperature is regulated either by a mechanical control valve actuated by the suction pressure and set to not allow the suction pressure to get below the value that makes the evaporator cold enough to freeze up, or an electronic control solenoid valve actuated by a control unit. Look for any connectors and wires on the back of the compressor to check if it's the electronically controlled version (if there's no wire and connector on the back, it's the one with the mechanical control valve). Either way, it sounds like the compressor is destroking too much once the evaporator gets cold. It may be a defective control valve or sensor.
Might also be some moisture stuck inside the AC piping that freezes the evaporator's thermal expansion valve's needle shut until it thaws out (and this also makes the compressor destroke), but it's unlikely, since there's a dryer.
Begin with having the refrigerant charge evacuated and weighed by a licensed professional, like Solar Mike probably suggested (pressure doesn't tell anything about charge weight and these compressors, especially the ones with mechanical control valves, behave erratically when the charge level becomes too low, and can also be damaged by the inadequate lubrication flow peculiar of a low charge condition). Then have the system thoroughly vacuumed and the correct charge level put inside and check for any improvements.