Unless you're getting an error message when the email is trying to be sent, ZC *is* sending the email.

But ZC has no ability to do anything about the message after it hands it off to the mail-delivery service on your server.
Sometimes those emails get lost in spam filters because they're short.

If you can't do a password reset by email, then do it manually: https://www.zen-cart.com/tutorials/index.php?article=2