In what way does it cut out?

Does it 'struggle' and die, do you hear the rpm increase even a little bit?

Normally, when you open the valve, the pressure will drop. This will result in the controller 'kicking in' and increasing the engine RPM and opening the inlet valve.

I don't know if this particular model as a digital controller or is the pressure set using a big control valve (usually on top or near the oil separator vessel).

Also, some newer compressors have an engine with electronic controls. Those are harder to diagnose. Others have the good old-fashioned mechanical control, where the engine rpm is controlled by control air and a lever/piston.

Please let me know and we will investigate further...

Cas