Hi Dustin,
I haven’t worked with Sendmail, so I can’t offer any guidance there. The contact form uses the standard WordPress wp_mail() function like most other contact form plugins. I took a quick look at the WordPress core code and it does seem to test for Sendmail, but I don’t know how well they work together. Given that the plugin uses a standard WordPress function, your issue is more likely with Sendmail and WordPress than with the plugin.
I would definitely turn on WP_DEBUG to see if any WordPress core code or plugins are causing an issue. If you see any errors in there that reference the plugin, please submit a support request on the WP-SpamShield support page, and I’ll be happy to look into it.
You may also want to test another contact form plugin like Contact Form 7 and see if you have the same issue.
I hope that helps!
– Scott