Hilwayb, go to your userCP (the leftmost link up on the blue bar above). Then, go to edit options. Down a little on the page that takes you to you will see all sorts of options for messaging. One of the options is a check box for whether you want to save sent messages. You probably just have that unchecked as of now. Once you check that (and then go all the way to the bottom of the page to save your changes), your sent pms will be saved.
Lots of other options there you may want to review as well.
Edit: was writing same time as you Apo! But anyway, if done in the userCP, no need to do it every time you write a pm.