Frankly I'm stumped.
I think disabling the add-ons is worth a try. It's best to test with IE's (No Add-on) option in Start > All programs > Accessories > System Tools > Internet Explorer, (No Add-Ons), and see how that works over a test period.
I am assuming that these web sites where this effect manifests are dynamic. What I mean is, they refresh automatically with new information.
Ahh, just a thought. You mentioned IE settings in your first post. How about in one of your computers resetting IE back to default? That's open IE, goto Tools > Internet Options, then the Advanced tab, then hitting the Reset button. This should remove all add-ons and I believe all 3rd party toolbars. See if that makes a difference.
Any other strange happenings on either machine, eg Windows Explorer acting up at all?