How important is it to distinguish relative risk aversion (RRA) from the intertemporal elasticity of substitution (IES) to understand bank liquidity provision and financial fragility? To answer this question, I develop a banking theory in which depositors feature Epstein-Zin preferences. In equilibrium, banks provide liquidity when RRA is sufficiently high (low) only for IES larger (smaller) than 1. Under the same conditions, banks might be fragile, i.e. subject to possible self-fulfilling depositors' runs. A time-consistent deposit freeze resolves banks' fragility if RRA is sufficiently low and IES is sufficiently larger than 1.