Cavity optomechanics implements a unique platform where moving objects can be probed by quantum fields, either laser light or microwave signals. With a pump tone driving at a frequency above the cavity resonance, self-sustained oscillations can be triggered at large injected powers. These limit cycle dynamics are particularly rich, presenting hysteretic behaviours, broad comb signals and especially large motion amplitudes. All of these features can be exploited for both fundamental quantum research and engineering. Here we present low temperature microwave experiments performed on a high-Q cavity resonance capacitively coupled to the flexure of a beam resonator. We study the limit cycle dynamics phase space as a function of pump parameters (detuning, power). Unexpectedly, we find that in a region of this phase space the microwave resonance is irremediably destroyed: only a dramatic power-reset can restore the dynamics to its original state. The phenomenon can be understood as an optical instability linked to the Kerr nonlinearity of the cavity. A theory supporting this claim is presented, reproducing almost quantitatively the measurement. This remarkable feature might be further optimized and represents a new resource for quantum microwave circuits.