Recent full hydrodynamic simulations of a sonoluminescing bubble interior have shown that the bubble content is compressed to a very dense state during the violent collapse. In this paper, we numerically studied the shape stability of a radially oscillating gas bubble by using Hilgenfeldt et al. theoretical model with corrections taking into account the gas density effect. Our results show that gas density variations not only significantly suppress the Rayleigh-Taylor instability, but also enhance the threshold of the parametric instability under sonoluminescence conditions.