@kworthington
I kept a browser on another computer with the old "forvever" cookie (before the site was moved). The symptom that this browser is showing is that when you first go to the forum, it shows the date and time as it should be. However, when I look at "show new replies to your posts" or "show unread posts since last visit" the date on the forum jumps back 2-3 days to when the cookie was last updated. At least I think the problem is the cookie.
Another related symptom that may help you troubleshoot is if it is one of these problematic comptuers, if you hit logout, a session error occurs and it actually refuses to log you out. If you try again, it logs you out, but after logging in you end up with the old date and time (in my case March 25th, 2013, 11:24am) (note is it now March 27th, 2013, 12:07:13pm as of this writing).