This procedure was complete for me and it resolve the issue. I supose that the problem is the number 1 below:
1. User name is just the first part of my email address, without the "@me.com" bit.
2. Password, of course
3. Incoming server: imap.me.com, port 993
4. Check "use SSL to connect"; uncheck the other two options under Incoming Server
5. Outgoing server: smtp.mail.me.com; port 587
6. Check override default port
7. Check Use SSL...
8. The "use incoming server info" bit that I wrote about earlier
That's it