The manage relational table behavior uses the value you set for the master key to lookup what options should be preselected.
When tyhe page loads, you are passing in a URL variable named email_id as the master key.
you should use that variable in the manage relational table settings. instead, you are using the EmailID form element which does not have a value when the page loads.
to fix this:
Open the bindings panel and expand the URL biding collection. check to see if there is a biding named "email_id". If not, click the plus button to create a new binding, select URL, and name the binding email_id
On the server behaviors panel, double click the manager relational table behavior to edit it.
for the master key value, change from using the EmailID form element to using the email_id URL variable.
next edit the forms action so that the email_id URL variable still exists when the form is posted.
action="messaging_email_update.inc.php?email_id=<?php echo $_GET['email_id']; ?>"