See: http://docs.sourcemint.org/firephp.org/firephp/1/-docs/Authorizing
Do you get any errors in the PHP error log?
Are you running a default install of Contao CMS or have you made any
customizations prior to including FirePHP?
Christoph
P.S. There is currently a bug in DeveloperCompanion that causes issues
when multiple browser windows are open. This will be fixed shortly.