Believe it not I think I just solved my similar problem. It seems a scary fix but it does work. Before you try my listed fix open Mail and make sure you have all your email from your Inbox saved locally on your Mac. So nothing should be listed in the Inbox. After you have moved everything from the Inbox then precede with my possible fix.
1. In Mail open Mail's Preferences and write down all the email server settings (to paper or a text file) because in the next step they will be blown away.
2. While still in Mail Preferences highlight the iCloud Account. In the Outgoing Mail Server(SMTP) use the edit function and use the - symbol to delete ALL SMTP server accounts (don't worry OS X will recreate this automatically). Once all SMTP account are delete proceed to step three.
3. After step 2, delete all the Accounts out of Mail then QUIT Mail!
4. Next open up System Preferences->iCloud (Make sure you are singed in and REMEMBER the name/password you used to sign in) and (once signed in) put a checkmark 'Mail & Notes". Then go back into the main System Preferences pane and select "Mail &Accounts". In that pane also put a checkmark in "Mail & Notes".
5. Open Mail and Mail's Menu items select 'Window", 'Connection Doctor' and make sure you get all Green dots on iCloud. If you get all Green dot by iCloud click on the red connection doctor menu bar to close it. Then open Mail's Preferences-Accounts and push the + button to add your other email servers information back in.
After these steps you shoud open Mail's Preferences again and tweak the email keeping sent messaages for days, weeks, etc. Just do mess with the SMTP server settings again. Hopefully this fix will work for your problem because it just worked for me. Good luck.