In neural implants, an analog-to-digital converter (ADC) provides the delicate interface between the analog signals generated by neurological processes and the digital signal processor that is tasked to interpret these signals for instance for epileptic seizure detection or limb control. In this paper, we propose a low-power ADC architecture for neural implants that process extracellular potentials. The proposed architecture uses the spike detector that is readily available on most of these implants in a closed-loop with an ADC. The spike detector determines whether the current input signal is part of a spike or it is part of noise to adaptively determine the instantaneous sampling rate of the ADC. The proposed architecture can reduce the power consumption of a traditional ADC by 62% when sampling extracellular potentials without any significant impact on spike detection accuracy.