Following up,
All of your repairs that I've looked at fail because the volume containing the archive spontaneously unmounts during the repair process. Here's an example of a repair that started at 09:49:
2017-01-21 09:49:40.052 -0800 Repair 5th backup.quanta
2017-01-21 09:49:40.052 -0800 archive: /Volumes/volume2/5th backup.quanta
Four hours later the volumes mysteriously, and spontaneously, unmounted. (Note that this doesn't appear to be associated with a sleep event.)
2017-01-21 13:34:42.401 -0800 unmounted volume /Volumes/volume2
2017-01-21 13:34:42.402 -0800 unmounted volume /Volumes/volume1
Not surprisingly, the repair starts encountering problems?about a million of them:
2017-01-21 13:34:41.999 -0800 problem getting volume statfs
2017-01-21 13:34:41.999 -0800 IO exception
2017-01-21 13:34:41.999 -0800 POSIXErr: 2
2017-01-21 13:34:41.999 -0800 Path: /Volumes/volume2/5th backup.quanta/repository.data
2017-01-21 13:34:41.999 -0800 ErrDescription: No such file or directory
This is most often caused by some intermittent hardware problem (failing drive controller, brief power interruption, flakey USB connection, and so on).
QRecall can actually be helpful in diagnosing this. Because the QRecall scheduler watches for volume mount and unmount events, it logs those when they occur. Filter out everything except the scheduler messages in the log, and then look for unmount events that shouldn't be happening. If your a command-line geek, this will also do the trick:
fgrep ' [3.' ~/Library/Logs/QRecall/QRecall.log* | fgrep mount