Outlook for Mac 15.3 (Outlook 365) gets hung up on Sync Pending

I have exactly the same problem. It appeared to start when I accepted the upgrade to Outlook 15.6. Have done a complete fresh install and still have the same issues.

Outlook 2013 works fine using VMWare.

Has anyone else linked the problem to the 15.6 update?

Yes! I'm having the exact same issues and now, with 15.6, I'm having a great deal of trouble downloading attachments automatically or otherwise.  I'm using Exchange.  

Microsoft at its worst...

HBR -- I found a solution to the sync errors:  go to your sent items and locate the record that's generating the error and delete it.  That worked for me.

After deleting Exchange account and set of of new, main problems are:

1. "Sync pending error" came back after a few hours after. Now have to restart Outlook to sent mail or make sure i have received recent mails. 
2. "Sync errors" continues - 4 logs per minute
3. Categories in Exchange calendar events disappeared after setting up new exchange account. Cannot set or edit categories any more.

Cannot continue to use a Outlook 15.x for Mac - for business!

Jason - I concur. I have no trouble so long as my MacBook stays "awake"--everything works great. As soon as it goes to sleep and then wakes, I get the "Sync pending" error and email ceases.

Still having this issue as well with 15.6, along with both my colleagues that are also using 15.6 (all on Yosemite, brand new Macbook Pro's). It seems that putting the laptop to sleep tends to trigger the issue. I also initially thought it might be tied to switching back and forth between a USB-based ethernet adapter and Wi-Fi, but I just tested it and doing so appeared to work fine.