I have two anchors positioned absolute on top of an image, the links are clickable in other browsers (Chrome, FF, Safari) but not in IE (tested in 8 & 9 so far)
IE has a nasty habit of not making links work as expected when they don't have any content. To fix this, give each link a for content.
Another thing to try is to set display: block; on the links to make IE flow them as block-level elements rather than as in-line elements. This can also help is you need the links to be empty.