I found the solution over on another site, however I felt I should post it here too.
Adding these header lines placates IE into allowing the download to take place over SSL.
It also doesn't appear to adversely affect the other browsers.
header("Pragma: ");
header("Cache-Control: ");
header("Expires: Mon, 26 Jul 1997 05:00:00 GMT");
header("Last-Modified: " . gmdate("D, d M Y H:i:s") . " GMT");
header("Cache-Control: no-store, no-cache, must-revalidate");
header("Cache-Control: post-check=0, pre-check=0", false);
Thanks daveyboy for your suggestions on this!
-Mce