My last completely successful O365 backup was 31/12/16 at 22:00. The job backed up 397 mailboxes without problem, and no configuration changes have been made.
On 1st January, 7 mailboxes failed, and the retries for those 7 mailboxes failed too. The failing mailboxes gave the error:
01/01/2017 22:49:43 :: Processing mailbox <email address removed> failed with error: Object reference not set to an instance of an object.
On 2nd January, 15 mailboxes failed with the same error, and the retries for those mailboxes also failed. Only one of the mailboxes that failed on the 1st also failed on the 2nd, so it doesn't seem particularly related to mailboxes. Either something changed in O365 over the new year, or the date change has caused an issue with the software.