This is not happening for me. I get scrobbles and play counts for a long time back, and they're all there.
If you close musicbee, delete users/*yourname*/appdata/local/musicbee/internalcache/LastFmPlayCountCache.dat, and reopen musicbee, it will (after some time) re-download your entire available last.fm history.
EDIT: I see you're on the Windows Store version (boo). I don't know where the file is for that version. Maybe the same place maybe not.
The only reason I can think of why it wouldn't pick up the play data is if you change the metadata it needs to locate the song in your library in between the scrobble and the sync. It would have no way to find the item in your library, obviously, if that's the case, because the item you told it you played does not exist any more.