Every widget that you connect with your Facebook profile receives the same token. When you disconnecting your profile from the Facebook app (by clicking "Disconnect" button in the widget) - the token gets revoked, and every widget that was connected using your Facebook profile lose connection to Facebook. So after that you need to go and connect all other widgets again.
If you want to delete some widget - just delete it without disconnecting it.
Please, don't forget to click "Save" button after connecting the widget.