Could you go to the Feedback menu in your dashboard, and check that submitted forms are saved there?
If they are, the problem is most likely with the way your server is configured to send out emails, through WordPress’ wp_mail
function.
Could you try to set up a plugin like Postman to send the emails through a different email provider, and see if it helps?
https://www.ads-software.com/plugins/postman-smtp/
If that helps, it could mean that although your server can send emails out, some of those emails are filtered out before they get sent out; your hosting provider should be able to check their server email logs to find out if the emails were blocked.
If none of this helps, it could mean that all emails coming from your site are filtered out by your email provider. If you don’t find the emails in your spam folder, you might want to try to send out Jetpack emails to another email address, and see if you keep experiencing issues. You can do so thanks to this option in the contact form builder:
https://jetpack.com/support/contact-form/#jp-carousel-723
Let me know if this helps!