I'm having the same exact issue with eshop and authorize.net. It appears as if we need to fix this ourselves. Lets get'r Done!
1) eShop shows correct shipping charges on confirmation checkout page.
2) Upon Proceeding to checkout page the (go to Authorize.net) shipping charge is missing.
3) It appear that the shipping charge NOT is properly transmitted in the order after redirecting to the authorize.net URL. and opening the page.
1) The problem is not at Authorize.net, as the problem starts during the class conversion when opening the URL.
2) All my Shipping charges, zones, tax bands, country codes, etc.. are set correctly.
3) I don not immediately see an obvious code issue (missing tag etc..)
pertinent lines of code are;
<form method="post" id="eshopgateway" class="eshop" action="'.$this->authorizenet_url.'">
$echortn.='<input type="hidden" name="x_line_item" value="'.$value.'" />'."\n";
So anyideas guys..