Gmail's Fetch feature will only grab emails from your First Class inbox that are received. It will not grab messages that were sent by you. If you want to save your outbox messages, you'll need to export them.
Highlight all of your messages either in your outbox or messages that show the word To: in front of the subject line and right click on them. In the dropdown, select Export. Chose a location that you can easily find again and it will export each email into it's own folder, now readable as a text file and a Word file.
