So its not the admin settings. If that works, normally the other should works too ( it uses exact same code to send mail ).
I think its pretty safe to say that either
1) the email provider ( gmail, yahoo, whatever it is ) is blocked by your host
2) the mail landed in junk maybe?
- if it does maybe the mail provider automatic delete junk mails?
Your best actions now are
1) Look what email address it was which requested reset password and ask your host if that provider is maybe blocked
2) Since you got the mail from admin email members, add yourself an test account and use the email you placed in admin email members.
Then request a reset password using that account