High harmonic generation (HHG) in many-electron atoms is studied theoretically. The breakdown of the frozen-core single active electron approximation is demonstrated, as it predicts roughly the same radiation amplitude in all noble gases. This is in contradiction with experiments, where heavier noble gases are known to emit much stronger HHG radiation than lighter ones. This experimental behavior of the noble gases can be qualitatively reproduced when many-electron dynamics, within a simple approximation, is taken into account.