I ran into the same issue, but I do not have jsFiddle in my application. Instead I wrote my own code that targeted to center a div popup box by accessing width, height, outerWidth, and outerHeight from the window object and the div popup box itself.
It is clear that the issue happens in IE8 browser, currently I am testing on version 8.0.6001.19019.
So I went ahead and implemented the fixings accordingly instructions above and it solves the case. My div popup box still is being centered hen I scroll the window down and up.
The very same issue was found in the more recent jQuery versions which means that bug prevents jQuery being cross browser compatible for IE8. Any new release of jQuery requires to be touched in other to preserve backward compatibility, until IE8 has being killed.
Here are the details where I implement that fix.
jQuery-1.4.2.min.js (line:144 Column:175)
jQuery-1.4.4.min.js (line:156 Column:251)
jQuery-1.7.1.js (line:8824 Column:31)
At the moment I am writting whit comment, jQuery-1.8.0 is already available for download. I inspected the code and it looks away different. I did not test yet, but comments about backward compatibility are in place.
Probably issue is fixed in the 1.8.0 version, anyway I hope this comment help people find solution for the bug when using old jQuery versions.