I read and tried many of the solutions to the sync issue people have suggested. None of which worked (turning on logging, locking the files etc).
However, i've solved for it for myself today, so I thought I'd tell you all what I did in the hope it might work for you too...
I opened Outlook in Windows (you could use OWA I guess) and complety emptied all subfolders in the "Sync Issues" folder. So empty out the "Conflicts", "Local Failures", "Server Failures" folders. Then I re-opened my Outlook 2016 on the Mac and the sync issue
pending annoyance is gone and mail is arriving without a shutdown-restart.
Of course it might start again..in which case I'll repost..but for now it is working. The syncing process was obviously getting stuck..
And: This is to a hosted Exchange server running Exchange 2010, not Office365.
Hope this helps anyone in the face of this bugginess and lack of support from Microsoft (as usual)..
JB