Please try disabling all plugins and check if the Theme Options are being saved then. If still not, please provide your admin login/password to firstname.lastname@example.org (no disclosure guaranteed) so that I could look at the admin code.
I’m not sure I understood – what you mean is that there was a plugin installed on your website that prevented Fuji’s Theme Options panel from saving the settings, and once you’ve disabled it the theme started working fine? If that is the case, could I ask you for the name of the plugin? There might be a compatibility issue that I must address in the future updates of the theme.