Not sure how it's set up here, but I believe the default setting for vBulletin is to NOT save sent PMs.
Go to Settings (top right), then My Settings (left side) > My Account > General Settings > Private Messaging > Sent Private Messages:
- Save a copy of sent messages in my Sent Items folder by default
- Don't save a copy of sent messages
Make sure that first boxed is checked then Save Changes at the bottom.