Deryl, I think I just stumbled over the solution for your problem by accident. I was doing some FSRecorder/Helicam tests and in order to have more control over the heli while filming I reduced the realism settings to minimum. When I switched back to the Cub and forgot to reset the realism to their max settings I experienced exactly the same banking problems that you described. The problem even occurs when the General Realism setting slider is only one tiny notch below max realism.
To cut a long story short: go to the Realism menu (Aircraft -> Realism Settings) and make absolutely sure that the General Realism slider is set all the way to the right.
YAHOO!!! That did it!!!
I thought I had all the realism settings maxed out only to discover that the "General" setting was a barely noticeable 1 notch below the max setting.
Glad to report the Cub now flies like a dream!