Mail in Mountain Lion "Incoming Mail Server" field cannot be empty

Question

I put my wife's email account which is in iCloud on mail with a couple of other iCloud accounts.  To identify who's iCloud account is who's, In the preferences on the account where you edit the description from the default "iCloud" to User's Name  iCloud and after you hit save I get an error saying The "Incoming Mail Server" field cannot be empty.  Yet is has p04--imap.mail.me.com in the field that is greyed out and I cannot edit the fields contents and therefore doesn't allow me to change the email account's description.  I've tried deleting the accounts, logging out of icloud, etc.  Nothing has fixed this yet.
On a side note, one of my other email accounts from iCloud keeps popping up with it needing the password field to be entered.  No matter what I try, it doesn't take the password.  I can log into it just fine through safari. 
So it seems like iCloud is having issues as well as Mail and contacting Apple twice and escalating to tier 2 both times has yeilded the person saying they didn't know and then hanging up on me.  Does anyone else know what I might try?

Answer 1

Okay, I had this problem and solved it as follows:
1. Deleted any non-functioning iCloud-IMAP accounts from Mail's Preferences. I had two that were working fine, so I left those in place. One of those was the primary iCloud account on my Mac, i.e., the account used for "Find My iPhone/Mac/iPad" and iCloud storage, etc.
2. Then I quit Mail and restarted my computer.
3. Went to my other devices and made sure the primary account was the same one there. [Note: It was not -- the primary iCloud account was different on my iPhone versus my Mac, I think this discrepancy might have been the source of the problem, but I don't know.]
4. I also made sure my wife's Mac uses a different primary iCloud account, one that is not on my machines, although we share one secondary iCloud Mail account (which is not the primary on any device -- it is always a secondary account).
5. Then, following MChannel's advice upthread, I went into System Preferences > Mail, Contacts & Calendars, and added the formerly problematic iCloud accout that way. I have everything turned on for my primary iCloud account. All of the secondary accounts only have Mail turned on (although I don't think that matters -- you can turn on the other features that are available there if you like).
6. Opened Mail and voila! -- everything is working fine. Accounts are all set up properly without me even opening Mail's Preferences.