... does it? Should each BES have it's own administration account / mailbox?

Simple answer, Yes. Here's why, for any environments with multiple BES:

1. Single points of failure are never good (if that mailbox is unavailable, no services will start / restart)
2. It is recommended to keep each BlackBerry users' mailbox close to the BES ... same goes for the administration mailbox
3. Do you have different groups managing different servers? Different accounts help with this management

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