I paused CloudFlare. When I do that it states that "Web traffic to this website is no longer receiving performance and security benefits. CloudFlare continues to resolve the DNS. You can reactivate CloudFlare for this website at anytime."
Are you having any issues with anything else that sends emails? (For example, lost password requests.) What sort of external service are you using?
There isn't a lot going on beyond the email sending stuff. It seems to handle the CAPTCHA validation, so I assume it's failing after that. I suppose it could be something getting confused on the server. Do you have the ability to restart the web server/PHP-FPM? If so, I would try that.
With regards to sending mail, I have some problems. Some new members are reporting that they are not getting their activation email. However, others are registering a new account with no problem and when I tested this myself, I received the activation email.
Thanks for your help. I spoke to my host about this and they said their firewall was stopping it from working. I didn't think the problem could lie with them as it was working previously. Looks like they changed some settings without my knowledge.