The random trips on this compressor - not being the initial startup, but when tank pressure needs to be topped off [restarting motor] really sound like:
<OL TYPE=1>
[*] Faulty Unloader Valve (not allowing pressure out of pump prior to restart),
if not, next could be:
[*] Start Capacitor with random short / open problem, or some other heat related problem with the Aux. (Start) circuitry,
and the last possible cause:
[*] Bearings on either the pump or the motor (or both).
</OL>
Sounds like an unloader problem. The random start or trip situations would be from where the piston stops. If it passed Top [is Top Dead Center correct for pumps???] after motor stopped, the cylinder would be heading into a vacuum state with the piston falling to the intake stroke, so no high pressure on piston in this position.
If the piston was heading up on compression stroke, then the cylinder has pressure against the piston, making it a hard start situation for the motor.
Just rambling on with my $0.02!
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Scott s.e.t.