.NET won't download full XML response from REST API

Question

When downloading an XML response from a REST API, I cannot get .NET to download the full XML document on many requests. In each case, I'm missing the last several characters of the XML file which means I can't parse it. The requests work fine in a browser.

I have tried WebResponse.GetResponseStream() using a StreamReader. Within the StreamReader I have tried Read(...) with a buffer, ReadLine(), and ReadToEnd() to build a string for the response. Wondering if there was a bug in my code, I also tried WebClient.DownloadString(url) with the same result and XmlDocument.Load(url) which just throws an exception (unexpected end of file while parsing ____).

I know for a fact that this API has had some encoding issues in the past, so I've tried specifying multiple different encodings (e.g., UTF-8, iso-8859-1) for the StreamReader as well as letting .NET detect the encoding. Changing the encoding seems to result in a different number of characters that get left off the end.

Is there any way I can detect the proper encoding myself? How does a browser do it? Is there somewhere in any browser to see the actual encoding the response is using (not what the HTTP headers say it's returning)? Any other methods of getting a string response from a web site with an unknown encoding?

StreamReader sample code

StringBuilder sb = new StringBuilder();
using (resp = (HttpWebResponse)req.GetResponse())
{
    using (Stream stream = resp.GetResponseStream())
    {
        using (StreamReader sr = new StreamReader(stream))
        {
            int charsRead = 1;
            char[] buffer = new char[4096];
    
            while (charsRead > 0)
            {
                charsRead = sr.Read(buffer, 0, buffer.Length);
                sb.Append(buffer, 0, charsRead);
            }
        }
    }
}

WebClient sample code

WebClient wc = new WebClient();
string text = wc.DownloadString(url);

XmlDocument sample code

XmlDocument doc = new XmlDocument();
doc.Load(url)