Denis Mitrowski
Did you check to see if there is any safety shutdown switches installed on that unit? High temp. shutdown, Low oil shutdown or perhaps a High air pressure shutdown. It sounds like your engine is working fine. Going by your description of the problem,my first suspicion would be the high pressure shutdown switch. The adjusting screw might be loose. Or the electrical connections to the switch are loose.

mike p
Sounds like pressure switch is faulty. What would cause it to shut off after filling with air is if it tries to load up compressor too soon with air in tank at or near cut off pressure, the motor can not turn compressor with a high load on output.