You need to designate which mailbox you want the sent mail to go to!
Create a 'Sent' mailbox, select it, and then go the the "Mailbox" menu. One of the menu items says "Use this Mailbox for" and you can select from Drafts, Sent, Trash, or Junk.
I had that same problem with Mail for a long time, until I found that menu option. And really, it's the right way to do it. Why should an application make the assumption as to what mailbox you want them saved under? Same line of thought goes for Drafts, etc..