You said "1. I closed Server A, the client tried to access Serevr A but on unavailability, shifted to Server B because it was the last server it accessed when a previous failover was performed." I might think about this a slightly different way and it may help see what is going on. Frequently, I have seen that when replication attempts point to a server that I did not expect, it is because the stacked icons point it to the unexpected server. The stacking order of icons reflects the relative order in which replicas were opened, I believe. While this doesn't help fix the issue, it might explain the behavior you are seeing.
Something else to check is the cluster.ncf file that is in the Notes client Data directory. It may still have information pointing to Server B as a cluster member (even though it shouldn't). You should be able to remove the cluster.ncf file and it will be rebuilt with the appropriate cluster members (Servers A and C).
Given all of that, I am not sure what the process is that a Notes client goes through when looking for a replica of it's mailfile. I would have thought that it would be: Home Server, Home Server Clustermate(s), Other Replica Server. If that is true, than your situation could well be explained by a confused cluster.ncf.
Cluster failover scenario (Wasif Farooqui 4.Jun.10)
Feedback response number WEBB864JLH created by William Eberle on 06/04/2010
. . Something to Check (William Eberle 4.Jun.10)
. . Free cluster manager tool (k berg 25.Aug.10)