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.
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....