I'm not opening the champagne yet, but I may have discovered the source of the problem. It is -- as a couple of you have suggested -- in Guitar Rig. I should clarify that I'm using Guitar Rig 3, the version bundled with Sonar a while back. Never bought the full version or any upgrades, because 3 seems to be all I need.
That said, I found a module nestled out of sight at the bottom of the GR interface labeled "OUTPUT." It has a control labeled "PRESET VOL," with a button next to it labeled "LEARN." I noticed that the preset volume knob
TURNS ITSELF ALL THE WAY DOWN WHENEVER I STOP PLAYBACK.
I had some trouble embedding this image, but you can click on it to embiggen.
I suspected the "learn" function was involved, and when I right-clicked on the volume knob, the dropdown menu included a "Clear" command. So I "cleared" it, whatever that might mean, and now the volume knob stays put when I stop playback or restart the track.
I don't recall ever messing with this control, and in fact the module containing it is scrolled off the bottom of the Guitar Rig UI, where I would not ordinarily be looking, however apparently I did something with it while in a trance. I'm cautiously optimistic that this is a real fix, but because of previous false positives I'm not ready to mark this thread "Solved" quite yet. I want to do more testing.
But that reminds me -- how do I mark the thread "Solved" when the time comes?
Thanks everybody, for your kind concern.