This usually happens if the email address specified in the mail_to parameter in the contact form is incorrect.
You may also check the error log file in your WP installation folder to see if there has been any errors raised after submission.
If this does not seem to be case, pls reply as a private message here with the site URL and a temporary login to the WordPress dashboard and I can take a look. You may also email me the same (see bottom right box in my profile page).