Looking at both your communities, you have both Display Name and Email Address login available. Could you please go to ACP -> System -> Login & Registration -> Methods -> edit each of your login providers that have form input (such as Standard, Converter, etc...) and ensure that both Display Name and Email Address are enabled?
The most common cause of what you're stating is that administrators have 2 login providers enabled that use the login form but the standard login provider only has Display Name or Email Address rather than both. Then on the other provider, it has both. Then in an example, user A comes along and tries to login with their email address but the standard login provider only allows Display Name, thus, a login error occurs.
If that does not help, please let us know which site in particular is the issue and verify the credentials on file are accurate. We can then look further.