Jetpack Contact Forms send out an email for each submitted form, and save each Feedback in the Feedback menu in your dashboard.
To do so, Jetpack, like other contact form plugins, uses a function named
wp_mail to send out emails to the post author, or to the email address you've specified when building the form. It's the same function that is used by WordPress to send you comment notifications, or notifications about new users registering on your site.
You can check if that function works properly by leaving a comment on your site and checking if you receive an email. Another alternative would be to use this plugin:
If you find issues with that function, you could use a plugin like this one to configure your WordPress installation to use a specific email service:
If the function appears to be work properly, it means that Jetpack's emails are filtered out before they can reach your inbox:
* They can be filtered out by your server before they even get sent out; your hosting provider should be able to check their server email logs to find out if the emails were blocked.
* They can be 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:
Let me know if this helps.