This failure occured while attempting to connect to the Principle server
You mention two key things in your post:


Mirroring
Work is being performed against the failover-server


I suspect what is going on is actually expected behavior.  Mirroring connection strings define both a Server (e.g. the Principal Server) and a Failover_Partner (e.g. the Mirror Server).  When establishing a connection to a mirrored database, if a connection to the Principal Server cannot be attained, an attempt to connect to the Mirror Server is then performed.

Per Connect Clients to a Database Mirroring Session (SQL Server):


  If a connection attempt fails or the retry time expires before it succeeds, the data access provider tries the other partner. If a connection is not opened by this point, the provider alternately tries the initial and failover partner names, until a connection is opened or the login period times out.


What I suspect the error is showing is the failed attempt to connect to the Principal Server because the database is actually active on the Mirror Server.  The error is thrown to your logs and then a successful connection is established against the Mirror Server because that's where the database is open/active.

This is expected behavior in a mirror configuration, and if you're able to (eventually) connect to the database, that means mirroring is working.  Take note that once you failover the database back to the Principal server, this error should no longer occur because the initial connection attempt to the Principal Server will once again succeed.