Thanks for your help MihChe!
Solution: wp_head function was missing from the template.
I did not originally build this site, but I do not see any plugins or other features that would be caching.
Yeah, that is the one I tried, but it seems like it will be a major hassle for the users.
Thanks for the info, I actually have switched back to using the form directly from the MailChimp for WordPress plugin, rather than Contact Form 7.
Second question, if you don’t mind…
Is there a way to add Google reCAPTCHA to the form? I did not see any option for that on the form. I have tried the CAPTCHA plugin add-on as suggested in the documentation, but I prefer to use reCAPTCHA