The first step towards finding the cause would be to figure out if the slowing down is in the browser or the server. From what you've said, I'd be inclined to think it's the browser (especially since the browser is IE
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Does this problem only occur when a user is logged in to the CMS as a user, or does this problem happen even if the user is just loading through page after page without being logged in? Is the problem always fixed by closing the browser, or does this slowing down sometimes persist even after the browser has been restarted?
If the problem is always fixed by restarting the browser and it happens regardless of whether or not the user is logged in, then it's almost certainly a problem with the browser.
If it is the browser, then the most likely culprit would be Javascript. When the slowing down starts to get bad, just close any tabs containing the site you're making without actually closing the browser. Just have another tab open on Google or something and then start trying to get your site to slow down in another tab. A lot has changed in browsers since I last did any amount of Javascript, but I would think that it is still true that all memory allocated for a site's Javascript should be purged when closing the tab. So if you can get your site to slow down and then speed back up by closing just the tab that it has been running in, and then opening a new tab and going back to your site in it then it'd go a long way to confirming that Javascript is the cause. Another way to check would be to go into Tools->Internet Options->and then untick the box for enabling Javascript. If your site stops slowing down after disabling Javascript then this will be a big clue.