How to Resolve "EWS connection error" for Specific Users in Message-Level Backup

When the NT AUTHORITY/SELF permission is removed from a user, 'EWS connection error' is generated in an Exchange 2010 Message-Level backup:
 

To resolve this error:

1. Log in to the Exchange server, and open the Exchange Management Console (EMC).
2. Expand Recipient Configuration, and click Mailbox.
3. Navigate to and right-click the user, and click Manage Full access Permission.
4. Verify that the NT AUTHORITY/SELF permission is missing from the list, and then click Add.
5. Type self in the search field, and click Find Now:
   
6. Click OK. The permission is added to the list:
    
7. Click Manage, and then click Finish to update the user permissions.