There was a similar thread
here a few months ago. You'll see that a user fixed a similar problem by changing the way the menus are hidden - looks like IE8 doesn't play nice when the menu is hidden via visibility:none - as here. So you could try changing your show/hide from visibility:hidden/visible to display:none/block or via a left margin.
Alternately, if this doesn't work, the links are OK in IE7 so you could as a fallback apply compatibility mode to the page via
<meta http-equiv="X-UA-Compatible" content="IE=7">
EDIT: Ah. From the Cufon css page
You can’t use visibility: hidden with elements containing Cufónized text in Internet Explorer 8 unless you set it after calling Cufon.replace(). In other words, visibility must not be hidden when Cufon.replace() is called. Other than that it is fine. There are no problems with display: none.