We investigate numerically the limits of the resonant magnetic response with a negative effective permeability mu(eff) for single-ring multicut split-ring resonator (SRR) designs up to optical frequencies. We find the breakdown of linear scaling due to the free electron kinetic energy for frequencies above approximately 100 THz. Above the linear scaling regime, the resonance frequency saturates, while the amplitude of the resonant permeability decreases, ultimately ceasing to reach negative value. The highest resonance frequency at which mu(eff) < 0 increases with the number of cuts in the SRR. A LC circuit model provides explanation of the numerical data.