WebRequest Over HTTPS Fails Under SQLCLR, But Works Elsewhere

I have some code in a SQL CLR stored procedure that calls out to a web service at UPS to obtain tracking information for a package.

The code fails on the last line, in the call to WebRequest.GetRequestStream(), with the following exception:

"System.Net.WebException: Unable to connect to the remote server ---> System.Net.Sockets.SocketException: No connection could be made because the target machine actively refused it
at System.Net.Sockets.Socket.DoConnect(EndPoint endPointSnapshot, SocketAddress socketAddress)
at System.Net.Sockets.Socket.InternalConnect(EndPoint remoteEP)
at System.Net.ServicePoint.ConnectSocketInternal(Boolean connectFailure, Socket s4, Socket s6, Socket& socket, IPAddress& address, ConnectSocketState state, IAsyncResult asyncResult, Int32 timeout, Exception& exception)
--- End of inner exception stack trace ---
at System.Net.HttpWebRequest.GetRequestStream()
at UPSTracking.TrackShipment(String TrackingUri)"

Here is the relevant code:

WebProxy proxyObject = new WebProxy();
WebRequest request = WebRequest.Create("https://www.ups.com/ups.app/xml/Track");
request.Proxy = proxyObject;
request.Method = "POST";
request.ContentLength = strXMLData.Length;
request.ContentType = "application/x-www-form-urlencoded";
StreamWriter sw = new StreamWriter(request.GetRequestStream());


This same code works just fine when not running in the SQL CLR assembly. The assembly is marked as External, but I've also tried marking it as Unsafe, which did not work either.

Any suggestions on what the problem might be or how to troubleshoot this further would be greatly appreciated.

Thanks,

Steve F.