By necessity - Server 1/primary node will become a secondary if Server 2 goes down. There is no longer a 'majority' available in the replica set (2/3).
You can force reconfigure the replica set to drop Server 2/secondary and Server 2/arbiter from the rs.config(). Essentially creating a 1 node replica set.
As per the documentation:
"Use this procedure only to recover from catastrophic interruptions."
The two server architecture you have is described is fine for a test environment. But you would never want to run that way in a production environment. Three servers would be a much better configuration. You can make the server for the arbiter much much smaller since it is not a data bearing node.
Cheers,
Jeff Sherard