I have a very similar problem, but with Apple's Mail, Calendar and Contacts at home. Mine appeared to begin about four months ago, after years of working fine. The home Mac will no longer properly sync Mail or Calendar or Contacts which come from the work Exchange server. The settings are all correct. In fact, if I delete the account and start over, it attempts to sync, and seems to work for a short period. Mail and events appear to begin filling up. Then, they suddenly stop, before completing the initial sync, and never work again. I have done this multiple times, and the result is always the same, but the stop point changes. I was testing it to see if it was a particular email or event causing the problem. That does not appear to be the case. My IT guys at work have tried to help using different routes to the servers at work. Same result.
My work issued iPhone has no problem, and my work based Mac, which ties into an all PC based, Exchange Server system works fine. It is only my home Mac that has this issue now. It is fully up to date.