Unexpected session reset when making authenticated user REST requests
Well. I found what was causing the error (unexpected behavior) reported above. There are chances that others might get stuck in a similar fashion, so I am answering my own question - 

The above resetting of Session was taking place because my service end point was not configured to work with 'authenticated sessions'. When creating a new service endpoint there is an optional checkbox labeled Session authentication with description Choose which authentication schemes that should be used with your endpoint. If no authentication method is selected all requests will be done by an anonymous user. which one needs to check so that web service resources created under that end point and allow authenticated sessions.

If you fail to check this checkbox at the time of creating the endpoint, you could do so later too, by editing the particular endpoint and clicking on the EDIT tab.