The stability of centimeter scale air bubbles is studied in quiescent suspending liquid under an imposed oscillatory acceleration field. Experiments were performed in reduced- and normal-gravity environments. A strong acceleration resulted in an instability leading to the breakups of the bubbles in both gravity environments. The breakup onset was investigated and found to be characterized by a critical acceleration a (cr). The influence of the liquid viscosity and the gravitational environment was studied. Empirical correlations for the onset are presented and discussed with the intention to reveal splitting mechanism. The inertial mechanism often deemed to cause the breakup of drops subjected to a rapid gas stream is shown to give explanations consistent with the experiments. A breakup criterion for both gravitational environments is proposed through discussions from an energetic point of view.