Hi bruce,
Sounds like the Send As error. You might not have set that one in AD when creating the new BESAdmin account.
You would see this in the MAGT logs as well as the Application Log:
[20265] (12/13 15:38:10):{0xFF0} {<user_name>@<domain>} MAPIMailbox::Send(ppMAPIMessage) - SubmitMessage (0x80070005) failed
If it's that exact error then Send As was not set or did not inherit down to the users.
Review the RIM KB on it, there's even a flash video on setting the permission:
BlackBerry Search Results
Hope it works out for ya!