Just had a similar problem trying to use SoapClient. Everything was working fine but in production, sometimes on page refresh, I would get the "SoapFault exception: [WSDL] SOAP-ERROR: Parsing WSDL: Couldn't load from .." error.
I was using the params:
new \SoapClient($WSDL, array('cache_wsdl' => WSDL_CACHE_NONE, 'trace' => true, "exception" => 0));
Removing all the params worked for me:
new \SoapClient($WSDL);