Security Kill Subscription Service

I am running a website for a newspaper. Every time I try to add any login security plugins it ends up locking our subscribers out of their online subscriptions. I am trying to find a plugin that will allow me to blacklist specific IP addresses that are continually using a robot to try to log onto our site. We use aMember Pro as our subscription to our subscription service. I do not know if that means anything to you, but I thought the info might help.
All I want is to get something in there that will stop these robots from trying to hack our site and that will not mess up the online newspaper subscriptions.