We present an analysis of a two-plane automatic balancing device for rigid rotors. Ball bearings, which are free to travel around a race, are used to eliminate imbalance due to shaft eccentricity or misalignment. Here we consider the effect that asymmetries such as support anisotropy have on the auto-balancing process. Stability diagrams show that the device is robust to the considered asymmetries when the rotation speeds are supercritical and the mass imbalance is small.