<p>Generic scalar perturbations on a fixed slowly rotating Kerr-AdS black hole background exhibit stable trapping, that is, the scalar field remains in a region between the exterior of the black hole and the AdS boundary for a very long time, decaying only inverse logarithmically in time. We study this effect employing fully general simulations that take into account the backreaction of the scalar field on the geometry. We find that the stable trapping of generic perturbations of Kerr-AdS persists at the non-linear level. Furthermore, at late times the spacetime settles into a time-dependent and non-axisymmetric black hole which differs from Kerr-AdS. Since our perturbations are suitably small and generic, our results indicate that slowly rotating Kerr-AdS black holes are non-linearly unstable.</p>