I spent whole day trying to get Magento SOAP API working with PHP SoapClient. No luck. As far as I can track down the issue its something in how Nginx parses XML output and changes endpoint in its response, so SoapClient cannot properly parse it and throws exception error.
Some suggested to change endpoint for request including index.php that Nginx throws in the XML response. No luck.
I even turned into nginx subs_filter and changed response, but still no luck dealing with SoapClient.
So I took the other approach and since I control Magento service I turned to Mage.php and wrote API myself. Worked out as much faster solution than SOAP.