We have a member of the board of directors retiring at the end of this year. Bank CEO wants to have this member remain on the audit committee after leaving the position on the bank board of directors. Since the audit committee is made up of out-side members of the board of diretors, shouldn't membership on the audit committee end when this person leaves the board?

I would ask the ex-board member, as they would probably no longer be covered under your director's and officer's insurance and may be taking on some pretty large personal responsibility if they officially remain a voting member on the audit committee.

The CEO must feel that this director has some expertise that is valuable to the committee. I agree with rl about the liability. Perhaps he could be an non-voting advisor to the committee. If he has any access after leaving the board I'd make sure he signs a confidentiality agreement as he will have access to non-public information without an official capacity to do so.