No wait... in templates/mg_themes/shoutbox_view_body.tpl:
Near the top of the file you have:
<meta http-equiv="refresh" content="120;url={U_SHOUTBOX_VIEW}?auto_refresh=3" />
So here it should be possible just to change the auto_refresh=3 to some other value...
and if you don't want it to refresh at all, I think you can just remove the ?auto_refresh=3 completely... though to confess, I've not fully explored how this works, since shoutbox_view.php doesn't even have a line for $_GET['auto_refresh']...
Examining shoutbox.php, there is reference to "auto_refresh" but it ought not to work at all, because it is accessed via:
isset($_POST['auto_refresh'])
Yet if it is parsed via URL string, it should be:
isset($_GET['auto_refresh'])
normally anything sent via URl cannot be retrieved via $_POST, I suspect at one time it may have been $_REQUEST, which parses a mix of GET and POST variables, but nowadays is not recommended lately through possible security holes...
So maybe this is a bug, but don't quote me on that just yet