We are currently running into a strange issue with Exchange 2013 and Outlook 2013. I am not sure if it is a limitation of Exchange or Outlook.
We have a system that is set up with Outlook 2013 so that all user mailboxes can be accessed by an administrator account. On the Exchange 2013 server we have been using "Add-MailboxPermission -Identity USERNAME -User adminaccount -AccessRights FullAccess" to enable this access.
In the past couple months we have run into an issue where two of the mailboxes can not be accessed. The message "The set of folders cannot be opened. Microsoft Exchange is not available. Either there are network problems or the Exchange server is down for maintenance." If I run "Remove-MailboxPermission -Identity USERNAME -User adminaccount -AccessRights FullAccess" and then run "Add-MailboxPermission -Identity USERNAME -User adminaccount -AccessRights FullAccess" I am able to access those two mailboxes, but two other mailboxes break. When I repeat the same steps with those broken mailboxes, another two break.