I was out of town last week, but got to take a look at the QDX again today. I found a manufacturing defect that was the source of the problem, and fixed it.
The fault was indeed with inductor L16, through which the VCC supply must flow to IC10 (the PCM1804). Here's what I was measuring:
The node labeled in red as 5V, at the bottom of C24, is where the circuit board trace runs from the right side of L16. So on one end of the trace, I was seeing the 5V that should be there. But at L16's right terminal, I was only seeing 1.7V.
Gently I pressed down with the multimeter probe, applying pressure to the top of L16's right side. The displayed voltage on the meter started to rise, and when it hit about 3V, the QDX's front panel LED flickered fast for 5 seconds, and it finished booting up.
So perhaps it wasn't ever properly soldered to that right side pad, and was only soldered on the left side. If it wasn't solder-bonded on the right, and only touching, that would explain why it worked at first. Then presumably at some point after those first few days, it got bumped or something, and that shifted the unsoldered contact far enough apart to introduce more resistance at that node.
Resoldering L16 (on both sides, to be safe) seems to have fixed the issue.
Leigh KG7WED