We investigate a banking system subject to repeated macroeconomic shocks and show that without deposit rate control, the banking system collapses with certainty. Any initial level of reserves will delay the collapse but not avoid it. Even without a banking collapse, the economy still converges to a consumption trap with positive probability. Savings are maximal in the consumption trap, but are used entirely to pay back obligations of banks. No long-term investments can be financed and GDP is minimal. We discuss stronger intervention rules that avoid both a collapse and the consumption trap, confirming that capital requirements are an early indicator signaling when intervention may become necessary. Our analysis provides an explanation why economies which experience a banking crisis may endure long-lasting economic downturns.