We discuss the effect that small fluctuations of both local anisotropy and energy density may have on the occurrence of cracking in spherical compact objects satisfying a polytropic equation of state. A systematic scheme to bring the fluid configurations out of hydrostatic equilibrium is revisited. Various models of polytropes arc considered, and it is shown that departures from equilibrium may lead to the appearance of cracking for a wide range of values of the parameters involved. Prospective applications of the obtained results to some astrophysical scenarios are pointed out.