Try adding a time to the email body. That will tell you if the web site is requesting the email to be sent at a later date or if it is the email server delaying the send.
If you just add:
sent:<?php echo(date('m/d/Y h:i:s a')); ?>
To the email body, that will include the date that the email was sent to the SMTP server. If that date is from a day or two before, that would confirm it isn't a problem with your script and that it is indeed an issue with the email server.