Unique problem - one channel silent under different variables

Bought a mint (looking) Cary slp 98 on eBay, connected to two reconditioned Hatachi HMA 7500 mosfet amps, work perfectly for years since reconditioning - biamping NHT 4 towers, bought new. 
When the preamp is turned on, a series of pops through the speakers, then Only the right channel plays. Switched tubes, didn't solve issue. Changed inputs from preamp to left and right amp and immediately both channels worked. Switched off, waited 5 minutes and still both channels working. Came back a few hours later, switched on again (having reversed the inputs to normal) and again same sequence: left channel silent and after switching inputs, both work and remain working until I switch off and come back when the units are cold.
I can understand that that there may be a resistor/capacitor that need to be hot before working, but why would switching input cables from left out to right input of amp and vice versa immediately fix it!
so every time I want to hear music I have to go thro this rigmarole! Why does switching cables fix the problem????
any solution will be greatly appreciated! I'm sure it will end up back at Cary but I wondered  if anyone (Almarg???) has an answer?  Does the popping on switching on, both channels pop, provide a clue?

I learned 20 years ago to  turn amp on last, off first. What makes you think I do all these cord exchanges with power on? Did I say that? No, I think you assumed it. With due respect, and I know you are being helpful, if I haven't learned that basic, I shouldn't be  wasting your time posting. Thanks for your input,
Thanks for your thoughts. I have found that if I leave the preamp on constant standby, the issue is resolved. It seems that the unit/tubes/caps/resistors work if kept "warm". Forgive my indignation at the thought of doing anything with power on! To me that's like driving s car with the hand brake on or playing with the innards of a 1500 w amp with the unit on and plugged in :)

It could be that one of the connectors on the cable is a little tighter than the other and one of the RCA jacks on the preamp is a little looser than the other.

When the right combination is used everything is fine, but if the (2) wrong ones are used, you drop a channel.

Maybe try a different set of cables from preamp to amp and see what happens.
Might be a problem with the left channel amp. Swap the left and right speaker cables and see if the trouble moves to the right channel.
Thanks for the clarifications, Denis.  Apologies if I inferred too much from your initial post (which I did). 
I have found that if I leave the preamp on constant standby, the issue is resolved.
That's obviously a key finding, but again it doesn't point to a specific cause as far as I can tell.  But have you done enough experimentation to be certain that what fixes the problem during the minutes following a cold start is switching the cables, as opposed to just disconnecting and reconnecting them, or not even doing that but simply cycling the power at the corresponding time intervals?

Best regards,
-- Al