Fortunately it is extremely easy to update your VirtueMart installation to make it do this.
FILE: administrator/com_virtuemart/html/basket.php
LINE: 147
REPLACE
$product_rows[$i]['update_form'] = '<form action="'. $action_url .'" method="post" style="display: inline;">
WITH
$current_stage = $ps_checkout->get_current_stage();
$product_rows[$i]['update_form'] = '<form action="'. $action_url .'" method="post" style="display: inline;">
<input type="hidden" name="checkout_stage" value="'.$current_stage.'" />
<input type="hidden" name="ship_to_info_id" value="'.$_REQUEST["ship_to_info_id"].'" />
<input type="hidden" name="shipping_rate_id" value="'.$_REQUEST["shipping_rate_id"].'" />
