From TechNote as per suggested by Tony :

During Exchange mailbox archiving, a mailbox archiving task is associated with each mailbox server. The mailbox archiving task processes only the active copies of the mailbox databases that reside on the mailbox server. Enterprise Vault does not archive from passive database copies.

When one database in a DAG fails, Exchange makes another passive copy of the database active. The mailbox archiving task that processed the failed copy continues to process the new active copy of the database until the Enterprise Vault's provisioning task runs. When the provisioning task has run, the new active copy of the database is processed by the mailbox archiving task that is associated with the new host Exchange server.

In practice, the failed database might be restored to its initial Exchange host before the provisioning task runs and updates the list of databases that are processed by each mailbox archiving task.