Some mail providers reject or drop the inquiry notification emails that Conversion Kit sends.
Why this happens. The notification’s From address defaults to the WordPress administration email unless you set a custom From address in Conversion Kit’s email branding settings. If the administration email is a free-mail address (such as gmail.com or yahoo.com), some mail providers reject or drop the notification.
What you can do. Set either the WordPress administration email or the From address in Conversion Kit’s email branding settings to an address on your own domain.