Coupon

I just tried on our demo website and it works the first time I click on the X.
Do you have some caching enabled on your website (in the joomla configuration or via the system cache plugin)?
Could you give a link to your website so that we can see that ?

I forgot to ask but we'll of course need a coupon code to look at that

Could you change the line:

<a href="<?php echo hikashop_completeLink('checkout&task=step&step='.($this->step+1).'&previous='.$this->step.'&removecoupon=1'.'&'.JUtility::getToken().'=1'); ?>" ><img src="<?php echo HIKASHOP_IMAGES . 'delete2.png';?>" alt="remove coupon" /></a>

by:
global $Itemid;
$url_itemid='';
if(!empty($Itemid)){
$url_itemid='&Itemid='.$Itemid;
}
?>
<a href="<?php echo hikashop_completeLink('checkout&task=step&step='.($this->step+1).'&previous='.$this->step.'&removecoupon=1'.'&'.JUtility::getToken().'=1'.$url_itemid); ?>" ><img src="<?php echo HIKASHOP_IMAGES . 'delete2.png';?>" alt="remove coupon" /></a>


in the file "coupon" of the view "checkout" vi the menu Display->Views and try again ?

I forgot a ?> in the first piece of code. It should be:

?>
<a href="<?php echo hikashop_completeLink('checkout&task=step&step='.($this->step+1).'&previous='.$this->step.'&removecoupon=1'.'&'.JUtility::getToken().'=1'); ?>" ><img src="<?php echo HIKASHOP_IMAGES . 'delete2.png';?>" alt="remove coupon" /></a>


to be replaced by:

global $Itemid;
$url_itemid='';
if(!empty($Itemid)){
$url_itemid='&Itemid='.$Itemid;
}
?>
<a href="<?php echo hikashop_completeLink('checkout&task=step&step='.($this->step+1).'&previous='.$this->step.'&removecoupon=1'.'&'.JUtility::getToken().'=1'.$url_itemid); ?>" ><img src="<?php echo HIKASHOP_IMAGES . 'delete2.png';?>" alt="remove coupon" /></a>

Since the shipping methods restrictions can be based on the total of the order, the shipping methods selection has to be reseted indeed.
If you want, you could have the coupon view on both steps:
login_address_shipping_coupon,payment_terms_confirm_cart_coupon_status_fields,end

For the fact that the coupon is not working properly, that's because we didn't thought about having that view on a step without the cart view. The fix is easy, just add the line:
$this->assignRef('coupon',@$cart->coupon);
after the line:
$coupon_error_message = JRequest::getVar('coupon_error_message','');
in the file components/com_hikashop/views/checkout/view.html.php