I had the very same issue.
For me the fix was as simple as wrapping the HttpWebResponse code in using block.
using (HttpWebResponse response = (HttpWebResponse) request.GetResponse())
{
// Do your processings here....
}
Details: This issue usually happens when several requests are made to the same host, and WebResponse is not disposed properly. That is where using block will properly dispose the WebResponse object properly and thus solving the issue.