Stopped sending confirmation emails on password reset

I have this weird problem: I’m using the Password Reset form, and it works fine for the most part. It goes like this:

• The user clicks on the “Forgot password” link.
• On the new page, the user fills in the information.
• The system sends a confirmation email, and it’s sent correctly (tested it at least 20 times, so I know it works fine).
• The user clicks on a link in the email they received and is taken to a page where they can choose a new password and confirm the new password.
• After this, they’re redirected to a new page with this message:

“We’ve just sent you an email. If you don’t see it, please check your spam folder.”

Now, the problem is that it’s not sending this last message anymore. I mean, it did for the first 3 times for different test users, then it stopped working altogether, even though I didn’t do any change whatsoever, it just stopped all of a sudden.

I tried creating new users, testing from other computers, using Private Browsing, but nothing. Everything else works, including the first email, so I know it’s not an SMTP issue either. It only happens at this step. I just removed the antispam filter just in case, but still nothing. At this point, I have no idea where to look, so any help would be greatly appreciated.