Check for WebForm Errors
The email may not have been sent without any error at the Drupal end. I recently experienced this problem, and found that the mail server was rejecting emails sent "from" someone claiming to be the same host as itself.

In short, Drupal could successfully send the email without knowing that it wasn't received. 

We solved the problem by installing the modules "mailsystem" and "mandrilL" and signing up for a free Mandrill account.