My guess is that something on the page is being requested over http. The authentication token over https is set to 'https only', so it won't be available to http requests. Requesting the http resource without the cookie will trigger the redirect to the
login page. I'm surprised it works in Firefox though.
I'd probably fire up 'Fiddler' to see what's being requested that's causing the redirect. You might also be able to find it with the built in IE developer tools (F12) network tab. You'll have to turn off 'Clear entries on Navigate'.