Including local automatic gain control (AGC) circuitry into a silicon cochlea design can be challenging because of transistor mismatch and model complexity. To address this, we present an alternative system-level algorithm that implements channel-specific AGC by using the output spikes of a spiking silicon cochlea. By measuring the output spike activity of each channel, the bandpass filter gain of a channel is adapted dynamically to the input sound amplitude so that the average output spike rate stays within a defined range. We evaluate the effect of our local AGC algorithm on a classification task where the input signal varies over a large amplitude range. Results on a task to classify speech versus noise show that a classifier trained on spike responses of a cochlea with local AGC maintains an average of 25% higher accuracy over a 32 dB input dynamic range, compared to the case when the AGC is disabled.