It seems that the problem only affects internet explorer and not Firefox either. Firefox can click and download the signed email attachments no problem.
I'm sure you have already checked these two items, but can you confirm what your caching policies are at Users>Resource Policies>Web>Caching and that IE does NOT have the option set to not cache SSL pages?
The caching policy should be unchanged or remove cache-control: no-cache|no-store.
The option to not cache SSL pages can prevent items accessed through the IVE from saving as they need to be cached in order to save.
My caching policies are set to unchanged and IE8 is set to allow saving encrypted pages to disk. It works fine in IE8 on the LAN, but not when the URL is rewritten.
When I compare the source url's in both browsers they are different. IE8 doesn't even get to the dialog box to choose the permanent destination for the file.
Thank you for the confirmation that it is with the ActiveX control by posting the URL and the other verifications.
Was the S/MIME control installed through the IVE or directly through the LAN? Does it make a difference?