Try dumping the session on a test page like:
<?php
@session_start();
var_dump($_SESSION);
?>
View source on the page to make it readable. Go through the process until the point where you would expect to see the shipping costs (confirm page) and then visit the test page in another window.
That should include any communication with your shipping service and any errors that might lead you to the solution. If you post FTP details and a URL to reproduce the problem I could take a look for you.
Did this help? Tips are appreciated...
