Ramakrishna,
Actually if you don't mind the Identify manager popup asking for username and password then you do not have to have a proxy setup. The proxy would eliminate the need for the user to login to use the secure services.
I just tested a secure service on my development machine using the 3.7 version of the viewer and my identify widget and I did not have any issue? So I am struggling to figure out how to help you further. It appears that the map service is local to your network and not public so I can not test your service.
Do you have any other map service layers that you have tried? Did they work?