Easily the biggest killer of compressors, the world over, is a failed unloader. The small innocuous device will allow connecting rods to bend and break, crankshafts to snap, motors to smoke, contactors to remove themselves from walls, and production to stop.
With a properly working unloader, starting a compressor motor is nearly trivial. The motor only has to spin up the flywheel inertia. With a malfunctioning unloader... Most compressors remain stalled until something lets go.
It sounds to me like your unloader is not doing its job.
The SS starts its cycle but since the compressor is improperly loaded the motor can not even begin to shove the pistons into a cylinder already filled with pressurized air. So the the SS continues to ramp the power, (big humming), while the motor's torque builds thru the start cycle. At some point you get lucky and the piston is forced thru Top Dead Center,(TDC), the inertia built up after that TDC is enough to carry the system thru the next compression stroke and so the compressor continues to run.
Your unloader is bad. You must fix it. The very next humming start could easily be the last one that motor will ever manage.
Flamin Systems, Inc.- http://www.flaminsystems.com