Hmm, I'm not seeing any issues. I have IE8 and running Windows 7 as well. Logged in, chose to be remembered, browsed around for a bit and closed the browser. Opened it back up went back to your site and I was still logged in.
Went through all of the cookies that are set and they all are being set properly with the correct values.
Curious if maybe there is some sort of IE8 security setting or something that might be getting in the way for you, although what that might be I'm not too sure. You might check your Private Settings in IE8 and see what it's set to. Maybe even try adding your site to the allow list and see if it makes any difference at all.
