How to send an email to the admin when user fails to login?
People mistype or use wrong alternate passwords all the time. Would be overkill to send e-mail on a first failed attempt. 

For security reasons, Drupal blocks user account after 5 login failed attempts.

You can use Rules Block/Unblock User to send e-mail when user gets blocked. (failed 5 times)


  This module adds rules events, as well as some default rules, for when
  a user account is blocked or unblocked.