The global financial crisis highlighted that the financial system can be most vulnerable when it seems most stable. This paper models non-linear dynamics in banking. Small shocks can lead from an equilibrium with few bank defaults straight to a full freeze. The mechanism is based on amplification between adverse selection on banks' funding market and moral hazard in bank monitoring. Our results imply trade-offs between regulators' microprudential desire to shield individual weak banks and the macroprudential consequences of doing so. Moreover, limiting bank reliance on wholesale funding always reduces systemic risk, but limiting the correlation between bank portfolios does not.