$query = "UPDATE table_name SET commentid = 'NULL', commentname = '$comm_name[$id]', commentmail = '$comm_mail[$id]', commentsite = '$comm_site[$id]', commentcomment = '$comm_comm[$id]' commentdte = 'NULL' WHERE commentid = '$id'";
$res = mysql_query($query);
Is the table_name really table_name, or did you probably mean $table_name?
Check all the field names, that is a common problem. If that doesn't work add:
echo mysql_error();
after calling mysql_query() and see what it tells you.