Can central banks afford to let a bank fail?

on 8th October, the EU finance ministers warned the banks and other financial institutions that they cannot expect to be bailed out by public funds if they are plunged into crisis by the credit crunch. Their underlying motive was clear that the institutions should not expect the authorities to bail them out using the public money. However historically we have seen that the authorities did intervene and prevented a bank failing because the effect of one bank failing may cascade on other banks leading to an adverse effect on whole economy.
Apart from issuing warning notes, the authorities should discuss the issue with the banks and financial institutions to mitigate any further losses and to make the system/processes more sound.