Hi Greg,
Based on current situation, we need to check if there is anything wrong with your Office 365 online mailbox account. Please take the following actions to check it out:
1. Add an email account of another mail service (Hotmail, for example) to your Outlook 2013 to see if the same issue occurs.
2. Try another network environment.
If the issue occurs to other mail services or other network environments, we can determine that this issue is about the Outlook client instead of the Exchange online services. It is recommended that you try to repair the Outlook connection to resolve the issue.
Thanks,
Allen Zhang