Seems like your session affinity or sticky bit not working correctly so it is doing a round robin for each web call. I am guessing your are getting routed to one midtier, you login there redirected to a new url , the next reroute is going to another midtier since that midtier did not have authentication it is asking for login again. As LJ mentioned turn off one off extra midtier and ARS and run with only one ARS and MT and see if you can login now. Also you could add in your /etc/hosts file on you midtier to map LB alias to local IP that way once LB routes to a server it stays there for that entire transaction.
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