Do you have a link to the site? It might help diagnose the problem.
I'm not sure but I think it may have something to do with the mega menu. Looking at the source of the contact us page I see the mega menu creates a form name="contact_us" which is the same name as the real (visible) contact us form on the page. I suspect it is somehow interfering in things.
Is it possible to turn that off briefly and then test to see if the problem persists?
Regards
David
Ah..I missed the 1.38 bit. I have to confess that I only tested the latest version with 1.39 and above. The original version worked with 1.38 (I think I remember testing it), if you wanted to give that a go. However upgrading to the latest version of Zen would be better, not least because of the security improvements since 1.38 was released.