Browsing through http://www.juicebox.net/support/wp-juicebox/ I have noticed that:
The following plugin is not compatible with WP-Juicebox. Please disable this plugin when using WP-Juicebox:
Contact Form 7
I have tested and indeed - after disabling CF7 juicebox work correctly.
However this is not a solution at all. Contact Form 7 is one of the best (if not best) contact page plugin.
This compatibility issue should be fixed asap. Till then I will have to disable Juicebox unfortunately.