1 - In Studio > SMTP Mailer, when you send a test email, does it work?

If so, have the user confirm there is not a typo in their email address. 

2 - The email address you've registered to 'send as' is it a custom domain, or a mainstream Gmail/Yahoo type?

Keep in mind, if they're trying to register a company or school email address, and you have a custom domain email as the sending address, the emails could be being filtered automatically. The business/school would have to 'whitelist' your domain if that's the case, or the user would need to use another email.