This article provides a known resolution to this issue on the Exchange server.
This issue was found on the Exchange side.
There is a component of the IMAP service called ImapProxy, and for unknown reasons can fall into ‘inactive’ state. Rebooting the Exchange servers may not activate the component. The only way to set it back to active is with a PowerShell command:
Set-ServerComponentState -Identity ex01 -Component ImapProxy -State Active -Requester HealthAPI.
This resolution can be found here: http://jetzemellema.blogspot.com/2015/02/issue-with-and-fix-for-broken-imap-on.html