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I've checked our mail logs and I see that you're receiving those emails because a spammer is filling the form since he/she is using the same email address to do this.
I see that you've already disabled the form which will prevent the form from being accessed. So you can modify your form with any of the suggestions above and re-enable it again.
Let us know if this helps.
My form users will be completing these forms over and over so your method will not work for me.
Any other ideas?
If you have the form embedded in your website, then you can ban the IP address of the spammer to prevent him/her accessing your site.
You can find the IP address in the submissions screen of your form.
If you want to try this method, you'll need to modify the .htaccess file on your website to do this blocking. Here you can find an example of how to accomplish this: http://kb.mediatemple.net/questions/1699/Block+a+specific+IP+address+from+accessing+your+website#gs