Using older versions of Outlook for Mac in business environments
I can't say that this will fix the situation for everyone, or ever be an option for many. When I installed the preview, I kept my 2011 installation active. I would use them interchangeably. I started having issues with the password prompt a few minor versions ago (I think as others have mentioned 15.8 was the last one that worked). I've tried a bunch of things to fix this and none of them worked. Yesterday I took the atomic option. I AppZapped Outlook.app, and then removed everything in the Group Container folders. I emptied the trash (some items were still in use and couldn't be emptied). Restarted the machine, emptied the trash again to make it squeaky clean, and then I reinstalled just the Outlook installer. With AppZapping the Outlook.app there were some configuration files that has to be regenerated by Outlook 2011 when I restarted that, but everything worked fine. So far, Outlook 2016 hasn't asked me for a password all day, even through multiple reboots. Now ... I have all my "On My Computer" archived email in 2011, so I could blow away all the content in the Group Containers. Your mileage might vary. Will report back if this issues comes back. I'm guessing this is one of the reasons why MS is finding it so hard to find the issue. Not sure of their test scenarios but maybe they're not testing update upon update (actually I'm sure they are) but 'in the wild' with all our different accounts, environments, etc, it can be a nightmare to track down the issue.
Good luck, hope this was of help to some of you.