I've done my searching, so please don't be too harsh if this has been covered somewhere already. Is there a "Sent Mail" folder where outgoing mail is stored? Specifically when using POP3/SMTP email.
Sent mail lives on the same screen as your incoming messages (with a check mark next to them). If you click on the message and save it, then it lives in the saved messages folder (again, with a check mark next to it) even after you delete your inbox.