If you have forgotten your username or password - there is a lost password link on the sign in page https://a.leaguerepublic.com/myaccount/login/index.html
When you receive your forgotten password email your username will be stated in the email with a link to reset your password.
Make sure you are using the username in the lost password email after resetting the password, a common problem is you entering an invalid username.
Your username is not necessarily your email address.
If the lost password service isn't working then contact a league admin for your site or another league admin for your site. Ask them to edit your record, remove your login, then invite you again.
LeagueRepublic won't help you get access to a site unless you are the only League Admin with access to the site because another league admin can sort the problem for you.