It sounds like your server might not be configured properly to send emails through the wp_mail function, which Jetpack, like other contact form plugins, uses. 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 the Check Email plugin and sending yourself a test email to see if it works? You can download the plugin here:
http://wordpress.org/plugins/check-email/
If you didn’t receive a test email, you could try using a plugin like this one to configure your WordPress site to use a specific email service:
https://wordpress.org/plugins/postman-smtp/
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. Another alternative would be to continue to use the Postman plugin, as it will allow you to bypass the filters set by your server, by sending emails from a different email provider.
- 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:
http://jetpack.me/support/contact-form/#jp-carousel-723
Let me know if this helps.