Ah I see. I have the same problem with some widgets for the theme I'm developing right now. I worked around this by outputting some default value, if the respective settings field is empty (or has not yet been saved).
It works now. The only thing I don't like is that the user gets logged out automatically, afterwards. Can you please make this optional?
Also, I saw that you added the unlink function to the Facebook plugin only. It would be great to have it for Twitter and Google, as well. :)