Messages you send are not saved by default - you have to click on the save box at the bottom of the message when you send it. We did that because sent messages count towards your pm box total and we used to have to answer a ton of questions why people couldn't receive mail because their boxes were full. Now this question comes up about once every 6 months instead.
If you want to see if someones getting the message click on the "request read receipt" box at the bottom and you'll be able to tell if the person read it or not.