Sounds like your CF7 install is not functioning correctly.
It is always possible that Contact Form 7 didn't install or update correctly on your site. It's a general problem with WordPress updates due to the unreliability of internet connections.
Delete the plugin folder at wp-content/plugins/contact-form-7/ using FTP (don't use Delete option on Plugins page as this may erase all CF7 forms) and install the plugin again.