If there are no errors with debug mode and maximum error reporting enabled then 1 of the following is happening.

1. Mail never reaches the mailer API (the email is never attempting to even send)
2. The mailer is never sending the outbound mail (it was sent to the mailer server, which did not send the email)

CB errors if the mail server can't be reached or if any of the mailer functions fails in any way, but you need to have debug mode and maximum error reporting enabled. If you get a success message when using forgot login then the mail was sent to the mail server, which is failing to deliver it for whatever reason and you'll need to talk to your host about that. If you don't see a success or error message then your template is probably suppressing Joomla notifications and you should retest with Joomla protostar remplate.