Hello,
What are you backing up at night? Is SQL installed on the media server or are you backing up a remote SQL server?
Follow the steps in the technote below and verify if the error messages in the event viewer stop after that:
Title: In the event viewer, Event ID: 57860 "An error occurred while attempting to log in to the following server... SQL error number: "0011"" is seen when backing up a server with SQL installed
http://support.veritas.com/docs/264616
Hope this helps. Do update us if the problem persists.
Note : If we do not receive your reply within two business days, this post would be marked ‘assumed answered’ and would be moved to ‘answered questions’ pool.
Regards.