Change mod_virtuemart_search.php from

<form action="<?php $sess->purl( $mm_action_url."index.php?page=shop.browse" ) ?>" method="post">
	<p><input name="keyword" type="text" size="12" title="<?php echo $VM_LANG->_('PHPSHOP_SEARCH_TITLE') ?>" class="inputbox" id="keyword"  />
	<input class="button" type="submit" name="Search" value="<?php echo $VM_LANG->_('PHPSHOP_SEARCH_TITLE') ?>" /></p>
</form>
to
<form action="<?php echo $mm_action_url."index.php" ?>" method="get">
	<input id="shop_search_field" title="<?php echo $VM_LANG->_('PHPSHOP_SEARCH_TITLE') ?>" class="inputbox" type="text" size="12" name="keyword" />
	<input class="button" type="submit" name="Search" value="<?php echo $VM_LANG->_('PHPSHOP_SEARCH_TITLE') ?>" />
	<input type="hidden" name="Itemid" value="<?php echo intval(@$_REQUEST['Itemid']) ?>" />
	<input type="hidden" name="option" value="com_virtuemart" />
	<input type="hidden" name="page" value="shop.browse" />
</form>