You can access your Spotify account on any number of devices, but you can only have offline synced playlists on 3 devices at one time. If you offline sync on a 4th device playlists will be desynced on one of the others. It sounds like this is what is happening here.
Technically, you aren't actually meant to share your Spotify account with anyone else. It's against the T&C. The reason for this is that sharing an account dilutes the income for the producers of the music listened too.