Why can't I read Http Request Input stream twice?

I was putting in some debugging code to test some things, and then the debug code didn't behave as expected. The example below is a simplified code to demonstrate my question.

This is in .NET 4 and using WebApi, I'm trying to print out the body of the http request in the debug code. To do this I seek the Input stream back and read the stream. It works fine the first time, but if I try to read it again, I get an empty string.

Why can't I seek back and read the InputStream a second time? In the example below, body2 is always empty. In the second set, CanSeek is still true and the the second call to ReadToEnd() returns an empty string overwriting the default.

using System.IO;
using System.Net;
using System.Net.Http;
using System.Web;
using System.Web.Http;

public class TestController : ApiController
{

    public class TestOutuput
    {
        public string firstRead;
        public string secondRead;
    }

    public HttpResponseMessage Post()
    {
        string body1 = "default for one";
        string body2 = "default for two";
        if (HttpContext.Current.Request.InputStream.CanSeek)
        {
            HttpContext.Current.Request.InputStream.Seek(0, System.IO.SeekOrigin.Begin);
        }
        using (var reader = new StreamReader(HttpContext.Current.Request.InputStream))
        {
            body1 = reader.ReadToEnd();
        }

        if (HttpContext.Current.Request.InputStream.CanSeek)
        {
            HttpContext.Current.Request.InputStream.Seek(0, System.IO.SeekOrigin.Begin);
        }
        using (var reader2 = new StreamReader(HttpContext.Current.Request.InputStream))
        {
            // this is always empty, even after seek back to origin
            body2 = reader2.ReadToEnd();
        }

        TestOutuput testOutput = new TestOutuput() { firstRead = body1, secondRead = body2 };
        HttpResponseMessage response = new HttpResponseMessage();
        return Request.CreateResponse<TestOutuput>(HttpStatusCode.OK, testOutput);
    }
}