Hi
i have a smiliar problem that's cost me a day's worth of unsuccessful troubleshooting.
QR ver 1.2.3.8,check for updates returns that this is newest.

Been backing up System Yosemite for several months.
Shame on me for not doing any test restores.
Shame on me for not doing dual backup to a QR competitor's application.

Finally the Mac Pro boot volume is causing problems to the point that a reformat restore is needed. Intent is to restore to a new virgin drive, not the problem drive.

My System Yosemite boot volume is incapable of allowing for the restore, but I attempted it anyway Source drive ---> target and it copied about 12000 files then stopped. Rebooting and trying again just resulted in QR crashing and crashing over and over.

Backup plan. I have a MacBook Air with System El Capitan and QR already installed. So I took the external source drive and external target drive, and with the MacBook Air in the middle, and QR would not open the Source backup file. Same situation David Ramsay encountered. So, i double clicked on the backup source file, and QR crashed. Next i dragged the source file icon onto the QR icon in the dock, and crash. Booted up Safe mode and tried again, CRASH

Next I moved the two external drives to a plain Jane virgin System El Capitan Mac Mini, installed QR and tried from there. Same as above. No open backup file, and crash, crash, crash.

David, you identified the problem last October; now it's almost February. A ton of man-hours awaits me to reconstruct everything from scratch. Finding out what the fix is, will be most appreciated.

Addendum, edit
The source volume checks out fine with Disk Utility Disk First Aid, it was new to begin with
and is error free.