Solids subjected to repeated cycles of stress or deformation can fail after several cycles, a phenomenon termed fatigue failure. Although intensely investigated owing to its obvious practical importance, the microscopic aspects of the initiation of failure continue to be pursued, particularly for amorphous and soft materials. The fatigue failure of glasses, in general of amorphous solids, with intrinsically disordered structures can not fit into conventional descriptions of that for metals.  Employing computer simulations of a model glass, we address the mechanism of fatigue. We investigate the characteristics of failure times, and the number of cycles to failure for shear amplitudes above the so-called fatigue limit.