Right under the PM that you're typing to send are Additional options. You need to check the following box before sending:
Alternatively, if you'd like to see every PM make it to your "Sent Items" folder, you can go into your Settings>General Settings and turn it on by default:
Please keep in mind that your "Sent Items" folder DOES take up your limited PM storage, and if you are getting "PM storage full" warnings you need to delete this folder as well.