What's your URL? A lot of times this is caused by an invalid Facebook application configuration. If you want to try something quick, try recreating a new Facebook application, only set the Canvas Callback URL and Connect URL as your home page. Leave everything else as default. Then use the new API/Secret key in JFBConnect.
See if this works, and if so, then start customizing your application as you need. Test regularly, and if you find a specific setting in the Facebook application that causes it to break, let us know. We've seen this happen before, but don't know what the 'magic' setting is that causes problems.