No it surely isn't way it's supposed to work.
But maybe a bit more info wouldn't be a bad idea so that we maybe can try to copy your procedure and see what happens.
Download as in making use of BS.Player's auto download feature?
BS.Player version? Type of video? Using which OS? How are settings under [Online subtitles]-tag at
(rightclick >) Options > Preferences > Subtitles (i.a. "Don't show available subtitle list ...")
Rendering mode used (under Preferences > Video [Video rendering]-tag).
By "restart" you mean full exit and start-up or ...?