No problem here whatsoever!
Just tested with build 808 (27 April 2004) and 2 CD version of Harry Potter.
One CD in PC's DVD-player and the other in PC's CD-player.
Also when playing another movie file after that, BSPlayer remembers position of subtitle.
Are you sure you're using BSPlayer's native possibility to display subtitles and that you are not (maybe unknowingly) using another program for that?