We have an estate of approximately 4000 machines with O365 E3 licenses currently using Office 2013.
Late last week users started reporting that they couldn't open documents from SharePoint Online in the Office 2013 applications. Users are prompted to sign in, but when they put in their credentials they are not accepted and the users are prompted again.
We have found that Office 2016 does not suffer from this problem (I guess because it uses a different authentication method). However our estate is in the middle of a complex migration process and upgrading all of our users to Office 2016 would definitely not be a trivial operation.
Is anyone else having similar problems? If so are they aware of any work arounds?
Also, have there been any recent changes to the O365 service that might have triggered this problem?
Not sure I can help but can I check just one thing, are you running any these Office 2013 versions -Professional Plus, Professional or Standard editions with Service Pack 1? Those are the only versions supported still, while support for 2013 versions of Office 365 ProPlus ended February 28, 2017, which you probably know already.
I would open a service request straight away if this is having a big impact and get confirmation of what the issue might be.