Some questions, that might be relevant if the problem turns out to not be a connection intermittency as the others have suggested:
1)Assuming the turntable is connected via RCAs, are the XLR input shorting plugs that were originally supplied with the unit installed?
2)What do you have the resistive loading set to? The reason I ask is that when you disconnect one of the turntable cables you are changing the impedance that is presented to the input stage for that channel from a low value (essentially the cartridge’s impedance) to a higher value (whatever the input loading is set to). And perhaps that change is allowing the input stage to recover from some abnormal condition.
3)When the dropouts occur, do you hear a relay clicking?
4)When you said "it actually is out when the system powers up" are you referring to before or after the approximately 45 seconds following turn-on during which the phono stage is designed to mute its output?
Regards,
-- Al