I realise that this topic hasn't seen a response for a long while now, but I can confirm the OP's complaints and can add that this occurs as an isolated incident regarding MusicBee. My experience of it, however, is of using the application on Windows 10 x64 for less than a week before seeing the exact same issue. It seems that the only workaround thus far is re-installation.
The problem occurred without warning for me. A song finished, then the active playlist wouldn't continue. Moreover, attempting to play anything else - including the song that just stopped after finishing - simply failed. To add yet more issues to this, I noticed that since the bug occurred, restarting the application takes significantly longer if it opens at all. Ending the process using the task manager usually has to happen before this, so it would seem that even closing the application goes awry.
This bug would appear reminiscent of a similar issue observed in older variants of Spotify, which had more or less the same effect of essentially killing the player and forcing a re-installation or alternative player.