Closing a gullible customer's account

Suppose that you have a customer that is 100% the victim of a scam. The transactions clearly show P2P withdrawals going to random people, the customer is purchasing gift cards at dollar stores and grocery stores and admits to sending this money to "a friend." The activity gets worse and worse every time you look at it, but the transactions are all authorized debit card purchases. Therefore, it is the customer's own money being spent, and the customer refuses to believe they are speaking with a scammer. Is this reason enough to close an account for suspicious activity? Is it a waste of resources for the account to be monitored?