It appears that IE6 has dropped support for Netscape style plug-ins. As a result if you have installed a third party tool designed to deal with ZIP files, and that tool has installed such a plug-in, then when you left click on a Download link you may end up with no download.
The easiest solution under IE is to right-click the Download link and select "Save Target As..." from the resulting context menu. Alternatively, you might also consider contacting your third party tool software vendor to see if they have a fix.