There is an unfortunate logic to bank runs. The rational thing for any depositor to do is to join in the run if there is even the smallest possibility that the bank really is in danger of failing. If you pull your money out and the bank survives, the costs of your mistake are tiny compared to the costs if the bank fails with your money in it.
Right now in Europe, there are trots — think of them as slow-speed runs — not on individual banks but on national banking systems.