Full error message:
Log Name: Application
Source: MSExchange Mailbox Replication
Date: 2016-10-04 09:06:31
Event ID: 1006
Task Category: Service
The Microsoft Exchange Mailbox Replication service was unable to process jobs in a mailbox database.
Database: Missing database (df16301a-89a5-4bce-bada-733a70c2ef90)
Error: Database 'df16301a-89a5-4bce-bada-733a70c2ef90' doesn't exist.
<Provider Name="MSExchange Mailbox Replication" />
<TimeCreated SystemTime="2016-10-04T07:06:31.000000000Z" />
<Data>Missing database (df16301a-89a5-4bce-bada-733a70c2ef90)</Data>
<Data>Database 'df16301a-89a5-4bce-bada-733a70c2ef90' doesn't exist.</Data>
This issue might happen if a mailDB was deleted in the past, but the server is still trying to proceed content in it. The solution as explained here is to restart the Microsoft Exchange Mailbox Replication service (which should not cause any outages).