Multiple passwords in keychain: Mac Mail keeps asking for password, then get 'unable to verify password'

This can happen if Mac Mail is more than one entry in Keychain for each in/out entry and it is using the wrong one.

In Utilities:

• Open Keychain Access,
• Use Keychain First Aid under the Keychain Menu item.
  Then either check the Password under that item, change it, or delete it and start over.