So.......there is good news, and there is bad news.
The good news is that I am almost certain that I know what the problem is.
The other piece of good news is that it wasn't due to me having any bad solder joints. ;D
The bad news is....I think one of my very expensive caps is broken. :'(
When I desoldered the caps to allow me to remove the chassis from the frame, I noticed that one of the leads to one of the caps was, for lack of a better word, limp. The ClarityCaps have fairly stiff solid core copper leads, but one of them was limp. I think the solid core of the lead broke within the insulation sleeving, very, very, VERY close to the cap itself (although the insulation is still intact). This is a real problem. If it were further from the cap, I would just cut the lead where broken and solder a new fly lead to the remaining piece of good lead on the cap. But the break in the lead on the cap is so close to the cap, that I suspect there is hardly anything left for me to solder a new lead onto, and I'm worried that the heat from the solder iron would damage the cap even if I tried.
That basically means I have no option but to try and return the cap, but I have doubts that they will accept a return where the tips of the leads show evidence of having been soldered. That probably means I spent $90 for a paperweight.
Since the lead is still in the insulation, which itself is intact, I think that when I turned the Crack over, the broken lead moved a bit within the insulation. Just enough to make contact. But when I turned it over and started playing music, after 10-20 minutes, the lead or cap would settle just enough to lose contact again. The cap would slowly discharge, which would explain why the sound would gradually fade out, rather than being a sharp break. Every time I turned the Crack over to try and diagnose the problem, the lead and/or cap would shift again, just enough to make contact. Then the cycle would start again: I turn on the amp, listen to music in both channels, but then the lead/cap settles in and contact is lost again. Etc., etc.
Grrrrrrrr.....I really hope Madisound stands behind their goods and sends me a replacement....