Thanks so much for getting back to me so quickly.
Emails are set up; new users are still getting emails to authenticate their accounts when they sign up. It seems to be just the reset password emails that don't seem to be working. Maybe it is a problem elsewhere within the SMTP server... I don't have Linux though. Is it something to do with the SMTP authorisation type? At the moment, this is set to 'LOGIN.'
Thanks for your help so far.