If you have to support IE 6 then you have to append the div element to the body and set the position as "absolute". Make the position attribute of the body element as "relative". And apply the rest of the styles suggested by reko_t. That should keep the div in the center as you scroll.
Apart from that, I would suggest you to consider one more case when you want to position some div in the center of the page. If your viewport's size is smaller than the div which you are positioning in the center then as you scroll you'll end up seeing the same portion of the div until you resize the window to be bigger than that of the div.
To solve this case, you should go for a javascript solution rather than a pure css solution. You should define a window resize listener. If the resized window's viewport is smaller then position the div in the left-top corner of the viewport and disable the onscroll listener. If the resized window's viewport is bigger than the div then your onscroll listener should apply the styles suggested by reko_t.