The electronic limit order book has transformed securities markets. Advantages of speed, simplicity, scalability, and low costs drive the rapid adoption of this mechanism to trade equities, bonds, foreign exchange, and derivatives worldwide. But limit order book systems depend primarily on public limit orders to provide liquidity, raising natural questions regarding the resiliency of the mechanism under stress. This paper provides an analysis of the stochastic dynamics of liquidity and its relation to volatility shocks using data from a futures market. Aggregate market liquidity exhibits considerable variation, and is inversely related to volatility, as predicted by our model. However, liquidity shocks dissipate quickly, indicating a high degree of market resiliency. This fact has important practical implications, particularly as regards to institutional trading, and market protocols. We explore these practical issues in detail.