It's not happening for us. Mostly Office365 email backend.

There's a 15.36 update out now so could be worth testing that.

I've worked with one person that has syncing stop with Outlook 16.34 and 16.35. Only solution was to remove and add the Exchange (on-premise) account. "Works right up until it doesn't." I haven't tried it with 15.36 yet.

I did try to reduce the message counts in various folders and subfolders, but I am worried the counts are still too high. I had hoped to have enough time to work with them on getting the root mailbox and all subfolders to below 5000 messages per folder and to not have folders more than three deep - I think those numbers are some of the suggestions I've seen.

Also, I haven't enabled logging, which might turn out to be the fastest way to uncover the problem: https://support.microsoft.com/en-us/help/2872257/how-to-enable-logging-in-outlook-for-mac

Thank you jhalvorson. Good to know I'm not the only one. We have about 5-10 people out of 300 that have the problem(or reported it).