The problem is that the function accepts the parameters <strong>$headers</strong>, <strong>$data</strong> and some others.

<?php
function drupal_http_request($url, $headers = array(), $method = 'GET', $data = NULL, $retry = 3) {
  ...
}
?>

and the same variables <strong>$headers</strong> and <strong>$data</strong> get overwritten within the function here

<?php
...
  // Fetch response.
  $response = '';
  while (!feof($fp) && $data = fread($fp, 1024)) { // <- HERE $data
    $response .= $data;
  }
  fclose($fp);

  // Parse response.
  list($headers, $result->data) = explode("\r\n\r\n", $response, 2); // <- HERE $headers
  $headers = preg_split("/\r\n|\n|\r/", $headers); // <- HERE $headers

  list($protocol, $code, $text) = explode(' ', trim(array_shift($headers)), 3);
  $result->headers = array();

  // Parse headers.
  while ($line = trim(array_shift($headers))) {
...
?>

then there is the check for the response code and if it is 301, 302, 307 it redirects by recursively calling drupal_http_request()
again with the parameters $headers and $data wich are no longer valid because they got overwritten.

<?php
  switch ($code) {
    case 200: // OK
    case 304: // Not modified
      break;
    case 301: // Moved permanently
    case 302: // Moved temporarily
    case 307: // Moved temporarily
      $location = $result->headers['Location'];

      if ($retry) {
        $result = drupal_http_request($result->headers['Location'], $headers, $method, $data, --$retry); // <- HERE is the call
        $result->redirect_code = $result->code;
      }
      $result->redirect_url = $location;

      break;
    default:
      $result->error = $text;
  }
?>