In actual fact, the problem is not the Disappearing list background bug. That bug occurs can occur when the menu is placed in a div that has the position: relative attribute. You are using a table based layout however, the menu is not in a div, it is in a TD Cell.
The real problem is that the menu_ie.css file for the menu to render in IE 6 is not uploaded tho the server.
make sure to upload the entire CSSMenuWriter menu writer folder to the server.
another problem i see on your page is that is missing the doctype tag. Add the following at line 1 to improve standards compliance:
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN" "http://www.w3.org/TR/html4/loose.dtd"><html>
also I see 2 charset meta tags:
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<meta http-equiv="Content-Type" content="text/html; charset=windows-1251">
one of them should be removed.