change the next link:
<a href="<?php echo $search_rs->getNextPageLink(); ?>">Next</a>
to:
<a href="<?php echo $search_rs->getNextPageLink(); ?><?php echo(isset($_POST['search'])?"&". $_POST['search']:""); ?>">Next</a>
then add the following at line 1:
<?php
if(isset($_GET['search'])) {
$_POST['search'] = $_GET['search'];
}
?>