Since Exchange 2007 the relationships between Exchange Servers and the Databases ( and hence users) they host is becoming increasingly tenuous.
EV's model of targeting an Exchange server for archiving is becoming increasingly anachronistic. The days when it was a reasonable assumption that there was a one to one relationship between a User, his mailbox, An Exchange Server, his archiving Server and probably his Vault Store are gone.
Trying to provide an EV System Mailbox with a consistent connection to an Exchange server is increasingly difficult when the databases are mobile. (Creating a separate Database, which is NOT in a DAG, and is DISABLED from failover, for the EV System Mailbox seems to do the trick)
It would seem a much better idea for Archiving Tasks to target databases (or groups thereof) directly. Thus EV would not care which Exchange Server any given database is on at any given time. Much as Exchange increasingly doesn't care which server hosts a database.