I'm sure the credentials is just stored in a session/cookie somewhere.
Cookies is kept per process, so it'll be per com-object.
Is there a logout button on the page you can click? If there's is a logout, make Powershell press it after you're done downloading the content and it should clear your session, enabling you do login the next time again.
You could also try to force-clear the cookies from the process by using:
InternetSetOption(IntPtr.Zero, INTERNET_OPTION_END_BROWSER_SESSION, IntPtr.Zero, 0);
See documentation on http://support.microsoft.com/kb/195192/en
You can also clear everything in IE by invoking:
rundll32.exe InetCpl.cpl,ClearMyTracksByProcess 4351