At the current moment, there is no method for administrator to know if there any attempt made by anyone to login into JIRA that has failed.

For example:

• currently the Maximum Authentication Attempts Allowed is set to 3
• when there are more than 3 failed attempt made, the CAPTCHA is shown
• however, administrator are not aware that there are failed attempt unless manually checking in the Users list

It's important for administrator to know especially if the username involved is used by REST client. This is because, the REST client will not be completed as it can't pass the value of the CAPTCHA.

Suggestion: send notification to administrator of username that has exceed the fail attempt so that administrator can clear the login attempt.