I'm in the same boat. In my case, "Remember Me" worked until I moved my front page from a subfolder of my domain to the root of my domain. When I did that, suddenly "remember me" didn't work anymore. Happens in Firefox, IE, and Safari - all three. So it's not an issue with my machine or browser, in my opinion.
I thought perhaps I needed a .htaccess file or something, so I put a blank one of those into the directory and gave it 755 permissions, but no luck.
I agree with the other user there seem to be way more questions than answers on these forums. It seems like very few proficient people hang out here compared to some other product forums I've seen. But we'll take whatever info we can get. I'll keep searching in case the answer is hidden in some other thread.