When trying to send emails from your site to yourself, it's recommended to use a third-party service like Postmark, Mandrill, SendGrid, or a similar service to avoid email failures.
These services require, or at least strongly suggest adding Headers to your server to say you're authorized to send them. When email clients such as Gmail see these, it'll likely send them to spam or possibly even stronger protections resulting in not receiving them at all.
In addition, another suggestion would be to use something other than the admin email address, like security@yousite.com, to avoid potential failures.