The previous companion paper described the motivation, design, and early experiments of a Magnetic Stereotaxis System. The part of the system considered in these papers is a helmet with a roughly cubic array of six superconducting coils used to apply force on small permanent magnet pellets in brain and in brain phantom material. This apparatus will be used to deliver drugs and other therapies directly into deep brain tissues, under control of a computer and fluoroscopic imaging system. Here, we analyze the general stability problems of controlling the currents in the coils for impulsive stepwise motion of the pellet, subject to quench avoidance in the superconducting coils, and in the face of Earnshaw's theorem governing stability in static magnetic fields. We also describe solutions that have been found to the primary difficulties limiting controlled pellet motion in the studies presented in the companion paper.