it is an issue of session. This is why Firefox works with you log into the site and then open additional tabs. the browser app is maintaining session. I would be surprised in IE7 didn't exhibit the same behaviour.
When you are creating those seperate browser instances within your application, each one is getting its own session, not sharing them. In this case, its requests from browsers that are important. when you say "Other requests, even from the same program, are redirected to the login page.", none of those requests are truly coming from that application, they are coming from the browser instances that the application contains.
Have you considered not using the browser control, but instead implementing some type of web service interaction or more pure http request/response type of interaction? I realize this may not be an option if the server you are interacting with requires some type of browser cookie.
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