2. Do you have any thoughts on what might be going bad and why?
There isn't enough info to even speculate. For example, if when it worked, it behave normally, such as same output level as the other channels when using test tones, then the cause could have something to do with the protection circuitry. In that case, a few factory default reset may (or may not as it depends) fix it.
Otherwise, it could be some defect in the preamp volume control circuitry, or as TLSGuy suggested, a bad solder joint. It is more likely the preamp volume, just guessing, because you said it would work when you turned volume up, if it is protection related that would not make sense but still possible because we would be talking about a defect.
The SR8012 is not cheap, so imo, it should be repaired especially if the seller would pay for it, even if only partially. That is if the issue is highly repeatable, if not Marantz may not be able to fix it without seeing it happens.