Perhaps IE9 is not cache'ing credentials, like the other browsers are. In the IE properties, there are settings for Cache'ing credentials and what not. I would compare those settings to those in the other browsers and see if they are the same.
What do your IIS settings look like? I know that there is a spot at the Server and site level to set authentication, like Forms, Basic, and Windows Authentication. This is getting outside my expertise, but I think you need to tweak those settings to Windows Authentication. I know that you can also do a Forms Auth, and have those creds pushed through to satisfy the other Authentication requirements. But like I said, this is outside me area of Expertise.
One last thing to check is the Group Policy Object and Local Security settings for Cached credentials. It is the setting that regulates how many previous logins are stored and passed through the browser. It is a bit of a reach, but it is someplace to look. The GPO may have a setting of Zero.