On the checkout_success.php and pp_checkout_success.php page, look for the following:
$clearThese = explode(",","OrderID,WA_Store_Cart_Items");
and change it to:
$clearThese = explode(",","OrderID,WA_Store_Cart_Items,WA_Store_Cart_FedEx_Quote,WA_Store_Cart_UPS_Quote,WA_Store_Cart_USPS_Quote");