Mail Quits on Mavericks
If you still have the old backup of the Mail database prior to the 10.9, you can replace the mail folder in ~/Library/ by the old version, and restart the Mail in your Mavericks. The new Mail will convert it to the new version of the database structure. 

I met the same issue a couple of days before, fortunately, I have the Time Machine backup, thus resolved by this way.