We establish that the effect of intensified deposit market competition, measured by reduced switching costs, on the probability of bank failures depends critically on whether we focus on competition with established customer relationships or competition for the formation of such relationships. With inherited customer relationships, intensified competition (i.e., lower switching costs) destabilizes the banking market, whereas it stabilizes the banking market if we shift our focus to competition for the formation of customer relationships. These findings imply that the proportion between new and locked-in depositors is decisively important when determining whether intensified competition destabilizes the banking market or not.