I traced the problem using the Event log. The system log had a "Warning"
(1116) that Microsoft Antimalware (Security Essentials) had found some
malware in a restore point, time: 21:48:35. The Application Event Log had
the entry (4104) indicating the backup had failed, time: 21:48:35.
I turned off System Restore (understanding that I'd be discarding Restore
Points and Shadow Copies), ran a full scan with Security Essentials, and
then turned on System Restore again. Next backup went through without
problems. (Your Mileage May Vary...).
I'm posting this for search engines, as I hadn't been able to find a clear
solution on the web, although many were posting the question. Hope this
helps.
Phil, London