Hi,
I've done some tests through your website and my question is : Did you change some file of your checkout view of your front-end template through "Hikashop->Display->Views" ?
Edit
After some other tests I think that editing the file
hikashop\components\com_hikashop\controllers\checkout.php, and changing this line :
$shipping = JRequest::getString('hikashop_shippings', null);
by :
$shipping = JRequest::getString('hikashop_shippings', '');
And this line :
if($shipping != implode(';', array_keys($cart->shipping_groups))) {
by
if($shipping != implode(';', array_keys($cart->shipping_groups)) && !(empty($shipping) && implode(';', array_keys($cart->shipping_groups)) == '0')) {