Error: "The Microsoft Exchange Server Computer is not available" when working with Exchange 2007 (33603)

When viewing the ESM logs from Archive Manager 3.7 you may see the error "The Microsoft Exchange Server Computer is not available"

This is a permissions issue. Do not use the Exchange Management Console to assign the ArchiveMGR_ESM user the Exchange Organization Administrator Role. This role by default is denied 'Full Mailbox Access' on all Mailboxes.
The ESM will not be able to process mailboxes if this is the case.

Remove the ArchiveMGR_ESM user from this group in Active Directory Users and Computers.

Assign rights to the ArchiveMGR_ESM user explicitly to the Organization through ADSIEdit.
1. Open ADSI Edit and connect to the Configuration Container
2. Navigate to the Exchange Organization: CN=First Organization,CN=Microsoft Exchange,CN=Services,CN=Configuration,DC=Domain,DC=com
3. In the Properties of the Exchange Organization grant the Account running the ESM Service Full Control

NOTE: In Exchange 2007 changes are cached by the Information Store Service. In order for these permission changes to take affect immediately it is necessary to restart the Information Store service.