A detailed study of sonoluminescence has been made in a high magnetic field. The intensity of emitted light depends critically on both magnetic and acoustic fields. In magnetic field sweeps at constant levels of acoustic drive, sonoluminescence disappears above a pressure-dependent threshold magnetic field. In sweeps of acoustic drive levels at fixed magnetic fields, the upper and lower bounds of forcing pressure that determine the region of sonoluminescence increase dramatically with magnetic field. A near-doubling of the forcing pressures is necessary between 0 and 20 T to sustain sonoluminescence. The pressure and magnetic field dependencies of sonoluminescence suggest that the primary effect of the magnetic field is to alter the condition for bubble stability with increasing pressure compensating for the effects of the magnetic field. This interplay between magnetic and acoustic fields reflects the importance of coupling between electronic and hydrodynamic degrees of freedom in sonoluminescence.