Apple - Can't archive mail on one of my Exchange accounts

I had the same problem. I went into Preferences > Accounts and deselected "Enable this account." Then, I quit Mail and restarted it. I went back into Preferences > Accounts and selected "Enable this account" and it all started working.

Rename the Archive folder on Exchange

Seems some sort of bad situation manifested itself between Mail and the Exchange server. I had to Rename the folder named Archive on the server to OldArchive, then attempt to archive a message and allow Mail to recreate the Archive folder. Then I copied all the mail in OldArchive to the new Archive.