If you need to log in every time you most likely need to configure whatever you're using to do the load balancing to allow persistant connections. It's hard to say exactly without know what exact equipment does your load balancing but you problem probably is there.
What's most likely happening is, you first go to the IP, and the you get "balanced" to Box A. Box A asks you to log in. You log in.
When you submit a request, for a new page, or anything else really, the load balancing devices sees this as an entirely new request and is now sending you to Box B. You've only logged into Box A, though. As far as Box B is concerned you're an interloper. So now box B asks you to log in.
Etc, etc.
Without know exactly what you're doing and with what equipment you're doing it with it's hard to say for sure but I'm willing to bet you need to change how you have your load balancing set up. If you don't mind saying, what kind of hardware are you using to balance? I've worked with a couple of the industy's mainstays for load balancing...I might be able to help.