On my pm sent box, it is not showing if my recent pm's are actually being sent out or not. It has shown some older ones but not the past three or so I have sent out over the past couple of months.
Click on Settings in the upper right corner. Find where it says "General settings".
Scroll down to where it says "Private messaging" and locate "Sent private messages".
Is the box where it says "Save a copy of sent messages in my Sent Items folder by default" marked? If not, click in the box beside that, and go to the bottom to hit Save Changes.