As soon as you change your password on Facebook.com you can not login anymore with your iPhone-App. Instead you’re getting a disconnect over and over again.
So what to do now?
Just visit: http://www.facebook.com/iphone and click on “remove app” at the lower left. Wait a few seconds (around a minute or two)!
Then grab your iPhone and DELETE the Facebook-App. Now reinstall it via the AppStore, start it again and login – voilà there you go.