Hi Fred,
Can you confirm what happens after you try and submit a second sign-up with the same email? Default behavior is a message should appear above the sign-up form asking them to confirm “You have already signed up for this task. Do you want to sign up again?” I suspect there may be a theme or other type of conflict that is suppressing this message. Can you provide a url where this is occurring so I can test on your site?
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If you can also confirm what version of the plugin you are running that would be helpful. Thanks!