My guess is that Mono implemented web requests slightly different concerning redirections (302, 303). Try disabling the AllowAutoRedirect flag to prevent the system to resend the request as a GET request.
HttpWebRequest postRequest = (HttpWebRequest)WebRequest.Create(address);
postRequest.CookieContainer = cookie;
postRequest.Method = "POST";
postRequest.KeepAlive = false;
postRequest.ContentType = "application/x-www-form-urlencoded";
postRequest.Accept = "text/html,application/xhtml+xml,application/xml";
postRequest.AllowAutoRedirect = false;