Elusive Tube-Amp Hum

This is my first post here, thank you for having me.
I'll try to keep this quick. Please excuse lower than average technical grasp.

For those who like puzzlers:

I have an Antique Sound Lab DT1001 which is a chinese manufactured integrated 50w/pentode zero-feedback unit with separate power, L&R output and choke transformers & 7AU preamp and KT88 power tubes.

I have had it for a year after buying it, marked down, with "cosmetic defect" from Audio Advisor.
From the start it has been a lemon for one single reason but I have kept it because of the amazing sound.
The problem is that a "60 Hz hum" will suddenly occur at any given moment and steps need be taken immediately to stop the hum. This symprom presents itself usually once only in every duty cycle/listening session.
There has never been a single commonality in occasions of the hum - it is utterly random.
It is always the same in both speakers and the same volume as the volume setting. One could call it a hum or a buzz. It sounds like an electric guitar pulled out from an amp. It makes me run to turn the unit off. The hum can occur when the unit is warming and no program is playing or it can hum the first time after 3 hours of playing music. Music can still be heard under the hum at diminished volume behind the hum.

It happens every listening session. It only happens once per listening session. (this is why I can manage to live with it).

I use only CD source - hum has occured with different players, interconnects, power sources, grounding scenarios and polarity scenarios.
I have switched everything that can be switched, (tubes) and taken it in (non-warranty) for review, touch-up and 3 days of play - at the shop the hum never occured.
The only thing different was the shop didn't take my interconnects. Which made me think.

So, when the hum occurs, I have been playing with the interconnects while leaving the amp on at reduced level. I think the problems - or some strong symptoms, lie here.
As I slip the interconnects (on the back of the amp, NOT the back of the CD player) around and on and off, I can get the hum to come and go, increase or decrease in intensity but never change from (what I believe is) 60hz.
Usually to get past this all by turning it off, letting it sit 10 min and starting over.

If you got this far I thank you for your attention and would appreciate you thoughts or questions,
Citizen