If you have opted to automatically backup your library to a remote storage service like Dropbox or Google Drive, OnSong may periodically attempt to access those services which can prompt for authentication.
To resolve this issue, you will want to disable automatic backup. To do this, go into the Utilities Menu (gear icon) and tap on the Backup option. This will open the Backup Screen. Here you can either turn off the automatic backup, change the frequency when the backup occurs, or change the export location to another service.
The other option would be to just sign into the service which should then prevent the authentication screen from appearing again.