Intrinsic localized mode (ILM) is spatially localized and temporally periodic oscillation in nonlinear coupled oscillators. We numerically investigate the dynamical stability of ILMs in a microcantilever array, in which ILMs were experimentally observed by Sato et al. It is found that the stability change of ILMs is due to the ratio in nonlinear potentials. This phenomenon also occurs in the array without harmonic potentials. Consequently, the stability of ILMs substantially depends on the ratio in nonlinear on-site and inter-site potentials.