When you put the drop down menus in a position: absolute div you will have separated the whole lot from the normal flow. I notice that the drop downs on the page you linked are quite deep, they must extend down below your position: absolute div, which may be why they are being cut off.
Is it possible to put some other content in the position: absolute div underneath? The drop downs will then extend over content which is also in the same div.
Or take the easy way out and get rid of the position: absolute containing div. Put everything in postion: relative divs. It should be possible to hold a div in a required position even then.
Code downloaded to my PC will be deleted in due course.
WIN7; IE9, Firefox, Opera, Chrome and Safari for Windows; screen resolution usually 1366*768.
Also IE6 on W98 with 800*600 and IE8 on Vista 1440*900.