Perhaps the stream is in several parts? In that case you will need to keep the stream playing in your browser and AUTO on until the browser sends the request for the next part.
Its not possible for JMR to detect and then download the same stream url at the same time. Many sites have multiple qualities/formats available and the player requests these depending on bandwidth etc. The urls are different. This is called adaptive streaming. If AUTO is on and the url is different it will be detected as a new stream. You can control this via the green thumb or switching AUTO off.
Debug logs and the site please if you are still having issues: