We propose a time-dependent slider-block model which incorporates a time-to-failure function for each block dependent on the stress. We associate this new time-to-failure mechanism with the property of stress fatigue. We test two failure time functions including a power law and an exponential. Failure times are assigned to 'damaged' blocks with stress above a damage threshold, σW and below a static failure threshold, σF. If the stress of a block is below the damage threshold the failure time is infinite. During the aftershock sequence the loader-plate remains fixed and all aftershocks are triggered by stress transfer from previous events. This differs from standard slider-block models which initiate each event by moving the loader-plate. We show the resulting behaviour of the model produces both the Gutenberg-Richter scaling law for event sizes and the Omori's scaling law for the rate of aftershocks when we use the power-law failure time function. The exponential function has limited success in producing Omori's law for the rate of aftershocks. We conclude the shape of the failure time function is key to producing Omori's law.