Unfortunately (or fortunate for me) I've never encountered any such problems, so I cannot reproduce.
However, I wonder what happens if you select "Remember last movie position" and also "Autoplay" (rightclick > Options > Preferences > General) and then - if your problem re-occurs again - you do NOT press [STOP] but just e[X]it BSPlayer "cold method" or press [Pause] and then [Exit].
If you restart BSPlayer after that, the movie should automatically resume playing exactly from the point where you left it (provided - of course - the moviefile is still in the same place where it was when you left playing it). This would seem a more acceptable "work-around" to me.
(It also works and is in fact intended for "normal" situations of course, where you just wish to quit watching a movie and resume later; e.g. maybe the next day.)