You reset the session variable based on a posted value that won't exist when the page submits to itself for an update.
You can probably just change line 25 from:
$_SESSION['birder_ID'] = $rsBirders->getColumnVal("Birder_ID");
to:
if (isset($_POST['ListofBirders'])) $_SESSION['birder_ID'] = $rsBirders->getColumnVal("Birder_ID");