We find that the flightiness of depositors displays pronounced fluctuations over time, reaching unprecedentedly high levels after the Covid-19 crisis. Elevated deposit flightiness coincides with low interest rate environments, expansions in central bank reserves, and a disproportionate increase in corporate deposits. Our dynamic model rationalizes these trends based on heterogeneity in investors’ convenience value, where those in the banking system value the convenience benefits of deposits more. Following deposit inflows from outside investors, e.g., due to QE's reserve expansions, the marginal depositor becomes more rate-sensitive and the risk of panic runs increases. Our findings imply that the risk of panic runs triggered by policy rate hikes is amplified when the Fed’s balance sheet size is larger, highlighting a novel linkage between conventional and unconventional monetary policy.