my email messages are saying they have been sent but aren't going through to recipient. What should I do?

In the Options menu of the compose message window, please enable both Delivery status notification and Return receipt. The first one will get you a report from the mail server about where your message has gone; the second is up to the receiving party. Hope this helps you further! Also is this just one person who does not get them? That might indicate a 'spam folder issue'. In that case, please verify if the messages are received when you use your webmail instead of your own Thunderbird.