In CutePlayer2.fx, I have
      onEndOfMedia: function() {
            myPlayer.currentTime = 0s; // rewind otherwise it stays at the end.
            bottomController.playButton.makeInitUI();
            println("onEndOfMedia called");
        }
in MediaPlayer instantiation. Basically back to the beginning at end of play.
This works constantly with 1.0 but not always with 1.0.1 b93.

Please try this:
http://fxsqe.sfbay.sun.com/fx1.0.1/CutePlayer2/FullScreenEnabled/CutePlayer2.jnlp

- Open the right tab by moving the mouse to the far end of the window frame.
- 2 FXM files are pre-loaded.
- Type in "http://fxsqe.sfbay.sun.com/resources/media/mixed/LewisClark_HiDef.wmv" (>200mb) into the Single Media URI textfield.
- Now you have 3 movie files. Select one to start play. Then click almost end of the progress bar to jump there. It will hit the end of the media soon and will go back to the 1st frame if successful. This wasn't always successful. When failed, I still see the printout, "onEndOfMedia called" but the frame remains at the end.

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The following uses 1.0 from dl.javafx.com
http://fxsqe.sfbay.sun.com/fx/CutePlayer2/FullScreenEnabled/CutePlayer2.jnlp
It always goes back to the beginning.