Microsoft will soon be disabling the ability to add new connected accounts to Office 365 and Outlook Online. This update will only affect Office365 Business accounts. This change will prevent you from being able to read or send mail from any email addresses that are not controlled by Office 365. New accounts will no longer be able to be connected starting September 15th. On October 30th all connected email accounts will stop syncing. This only affects the Outlook online web application and will not affect your ability to use the Outlook application installed on your computer.
While this change may be alarming Microsoft has a few suggestions, which can be in found in this article which will allow you to continue to see your other emails: link