Are you able to create restore points and physically check they have been made ?
The Windows Repair program does repair the Volume Shadow Copy service which could be at fault, but if you can create restore points, then I don't think that would be a consideration.
Can you try the back up again and then go immediately into Event Viewer, ensuring Event Viewer (Local) is highlighted in the left pane - if it isn't, just click on it.
When it has read the data, click on Error then on View All Instances of this Event in the lower right pane and see if there are any additional errors with the same time stamp which may be associated with the back up error.
If you think any are relevant, you can copy & paste them into your reply by clicking on one then on Copy/Copy details as text in the lower right pane - right click in the Reply box and select Paste and do the same for any others.
I'm not sure if a sfc /scannow run from an admin command prompt would find anything on this but let me know if it reports anything other than no integrity violations.