If you are having this error at the page: "Request do not pass security check! Please refresh the page and try one more time."
then this error is appearing, when NONCE field in booking form was not updates, and there some old value.
Nonce field its hidden field in your booking form with unique value, its required for the prevent of the remote (CSRF/XSRF) attacks to the booking form at your website. Its standard practice for all forms in WordPress.
The only reason why it’s can be, because of some cache issue.
1) Usually its because of cache issue at your server, because of Cache plugin, or because of some cache system/software/tool directly at your server.
Please recheck for the any cache plugins, like "WP Super Cache" or "W3 Total Cache". If you are using someone, please deactivate it or add the exception to the page with booking form for do not cache this page(s).
2) If you still will have an issue so then please try to deactivate one by one all your active plugins at the WordPress > Plugins menu and make testing after each plugin deactivation. If its not help, please deactivate all your plugins and active the default WordPress theme. And then retest it again.
3) The other reason can be caching of the website directly at your server. In this case you need to contact support of your hosting and recheck about the any caching software or tool at your server.