I’ve had the same issue: The Connection: Keep-Alive header is not sent except the first request, and the server I accessed won’t give me the correct response if it is missing. So, here are my workarounds to this issue:
First is set the ProtocolVersion property of HttpWebRequest instance to HttpVersion.Version10. Except the http command will become GET xxx HTTP/1.0, it works and uses only the public API.
The second way uses the reflection to modify the internal property ServicePoint.HttpBehaviour of HttpWebRequest instance, like this:
var req = (HttpWebRequest)WebRequest.Create(someUrl);
var sp = req.ServicePoint;
var prop = sp.GetType().GetProperty("HttpBehaviour",
BindingFlags.Instance | BindingFlags.NonPublic);
prop.SetValue(sp, (byte)0, null);
req.GetResponse().Close();
Hope this helps.