Have you tried the CVI SendMail.c example project? The send mail example includes a GUI that provides a control for selecting files for attachment and sends an e-mail. It would be interesting to see if the NI example code fails also.
Have you tried using a e-mail client like Outlook Express on your target system to send the same attachment to the same destination? If that fails, then it's some other problem than the CVI application.
Menchar