Manager::checkAuth in manager.cpp will cause a Primary to step down if there is an auth failure, and no nodes are marked as up. This is primarily during a reconfig so that the authentication problem would get attention from the user - however it has also been seen to bring down a otherwise functioning Primary in a replica set.

There doesn't seem to be a benefit to stepping down on auth errors, especially in the case were a node has been operational as Primary for some time.