Hi,
Mezzmo transcodes the file to 10 second segments for delivery to the Roku, possibly the Roku is requesting the same segments or Mezzmo is creating extra segments when transcoding. Can you please try playing a file that has already been transcoded or pre-transcoding a the file http://www.mezzmo.com/wiki/doku.php?id=pre-transcoding_files&s[]=pre&s[]=transcode to see if the repeating issue still occurs?