A bank is a place of safety. Of security. Of reliability.
That is, until the nukes start falling.
In Alas, Babylon, the downfall of the local bank provides a prelude to the struggles that will befall Fort Repose. At first, the bank's owner, Edgar Quisenberry, thinks that this'll be another passing crisis: people will take out some money, relax, and then the federal government will step in to fix up everything right and dandy.
It's not until Edgar tries to contact the central bank in Jacksonville and discovers that Jacksonville no longer exists that he understands the gravity of the situation. Yikes. What a wakeup call.
It is, for him, the end of the world. Take a look:
There was a phrase he had heard a number of times, "the end of civilization as we know it." Now he knew what the phrase meant. It meant the end of money. (5.228)
In this way, the downfall of Fort Repose's bank represents the broader downfall of American society. Like the government, schools, and even the police, the entire financial structure of the United States collapses in one moment. As we later see, the survivors do indeed pick up the pieces and rebuild among the wreckage, but the society they'll construct will be drastically different than the one they left behind.