Hello.
Please recheck for any cache plugins, like “WP Super Cache”, “WP Fastest 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).
Otherwise probably it’s because of conflict with some other plugin or actual theme.
Please try to deactivate one by one all your active plugins at the WordPress > Plugins menu and make testing after each plugin deactivation.
If it does not help, please deactivate all your plugins and active the default WordPress theme. And then retest it again.
We just need to find the reason for this issue.