I has been posted in this community and I have the same problem of Outlook For Mac 15.6 not synching, this time with an exchange corporate account, without a restart.
For example if I send a mail, and look at the Sent Mails it's not there, but the mail is sent. If I restart I get new mails, but between restarts there are no refreshes, even if I press the Send and Receive button.
I'm using my Outlook for Mac with a Corporate Exchange server. I have no problem with Outlook 2013 for Windows, only Outlook for Mac 15.6.