Why does unplugging/replugging TT leads from tube phono pre-amp reset dead channel?

It's more likely the preamp has a loose RCA plug / cold solder joint.

Cold solder on one channel, but alternating right and left?

Have you tried another set of phono leads?

Maybe there is a member of our group in your area who would be willing to allow you to connect your phono preamp to their system and rule out that possibility

As others have said, clearly the movement (wiggling) caused when you attach or detach RCA plugs to the sockets is causing something to touch and hence reconnect.

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