Larry Jones
The good news is, if I misled you about that, you're off the hook for not figuring this out. 

Actually, I think I had figured it out...that's why I asked about Guitar Rig initially . I wrote the manual for it, so I'm pretty familiar with ways it can go wrong as well as ways it can go right.

Hey - Don't feel bad.
 
I had a crowd of friends watch me in high school, as I spent 20 minutes jimmying open the locked driver's door, of my car, and nobody said a word until they laughed hysterically, as I discovered that the passenger window had been WIDE OPEN the whole time.
 
Everybody has a DOH moment or two.
 
Bob Bone
 

Anderton
And we STILL don't know for sure it is Guitar Rig...it just looks likely.

Looks very likely to me.
I opened a new project (Normal template). Recorded electric guitar with no plugins or FX of any kind. Played it back. Stopped, started, volume stayed the same. Added another audio track, this time with Guitar Rig, using the saved settings from the two projects which were giving me trouble, and recorded some electric guitar (NOTE: I had a custom preset in Guitar Rig that I was using in both projects, and I used it for this test). Played it back -- so far, so good. Stopped and restarted, and the volume knob on the GR OUTPUT module turned itself all the way down and the volume of the playback almost vanished. This is obviously something that I did to myself, but I don't know why. Probably I clicked something a couple of days ago, it didn't seem to have any effect, and I forgot about it.
 
HOW I "FIXED" IT:
I "cleared" the "preset volume" knob in Guitar Rig (details here) and re-saved the custom preset. Deleted Guitar Rig, re-inserted it and went to the newly saved preset -- all seems to be well.
 
I think my problem is solved. As Craig Anderton has said, the good news is I'll recognize this issue if it ever comes up again.

Anderton
We still have no idea WHY the preset volume is changing, if in fact it is. IIRC GR can't be receiving MIDI data and acting on (e.g., a misdirected output from a MIDI track). So I haven't solved anything, I've just pointed to a promising clue. Maybe. I think...

The preset volume was definitely changing. Once I scrolled down to expose the Output module, I could see the knob turn itself down when I did certain trigger actions, such as stopping playback. And once it was down, it stayed down until I manually turned it back up. I'm guessing it has something to do with the "Learn" button right next to it. All of this was happening (at first) out of sight, because the output module was below the bottom of my Guitar Rig window. I read a review a while back that said Sonar really needed a high pixel-count monitor, and now I can see why. I am using two monitors with native resolution of 1280x1024. In a high-def resolution I would have always had all the Guitar Rig modules showing, and who knows? That little twirling knob might have caught my eye sooner.

Larry Jones
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.

I'm glad you got this worked out!   And I, for one, am now very aware that these controls exist (probably never would have been aware otherwise).
 
But more important...   do you mind if I use "embiggen" at some point?   It's my new favorite word of the day.