This is because you have unknowingly kept the "Keep me signed in" option checked while signing into the face book.
You can try Signing out maually and then while logging in back keep that option unchecked.
If that does not wotk then you will have to clear saved password.
- Click Tools > Internet Options
- Click the Content tab
- Click the AutoComplete button
- Uncheck Usernames and passwords on forms and Prompt me to save passwords if they are checked
- Click the Clear Passwords button
- Click OK to confirm
- Click OK and OK again to exit