iCloud/iTunes Account Locking out Active Directory Account [?]

😐

The facts:

• I have been having this problem for the past four+ months.
• My work email address is my iTunes account name
• My work AD account gets logged out most evenings, sometimes within an hour of leaving work, sometimes late at night
• I know when my account is logged out because my iPhone will ask for my Exchange password, or I cannot get into Outlook Web Access
• When my iTunes/iCloud account password is the same as my Active Directory password this does not happen. When this was the case earlier this year I went 90 days without a lockout. The day after my password expired and I changed my password - locked out again
• Exchange recognizes two mobile devices, my iPad2 and my iPhone 4, as mobile ActiveSync clients
• I have reset both of these devices, updated to the latest iOS and reinstalled and reconfigured my apps
• This occurs even when neither of these devices has an active ActiveSync account set up to use my work Exchange server
• The keyrings (Mac) and Credential Managers (PC) of all my home machines have been sanitized
• Mail (Mac) and Outlook are not configured on my home machines, and they are not affiliated with the work domain in any way

😮

From these facts it seems to me that the issue is:

• There exists a machine attempting to reach my Exchange account using a password I have used in the past
• If it is a computer that I have possession of, it must be an iDevice, because this behavior has still occurred when all others have been powered off
• If it is an iDevice under my control then it is something in iCloud/iTunes, because it does not depend on having the Exchange account configured on either iDevice and those are the only applications with knowledge of my work email address

So,

If it is my iCloud/iTunes account then WHY in the name of all that is sacred is it hitting my work Exchange server and locking out my account?

😕

I can think of no other -possible- devices or online services that have both that password, and knowledge of that email address. I remotely wiped an old phone that might have had the email account configured.

Help?