I was thinking there was a way to select (in settings, perhaps?) that you would like to save those automatically. Just sure, but worth a peek around your profile set up. There is a limit to the number of PMs you can have though -- and the saved 'sent' ones will be counted in the number. Just so you know.
Opps, the above is not where you select this option. I went and found how to do it. It is when you send a PM (before you hit send) at the very bottom there are boxes and you can check the "save a copy of this message in your Sent Items folder".