It's a good idea to appoint a Successor Agent when signing a Power of Attorney. This is even more so with a Durable Power of Attorney, which is meant to be in effect for a long time. Then, if the Agent should at any time become unable or unwilling to perform the responsibilities of the contract, an appointed successor is already lined up to assume responsibility.
For example: A man appoints an elderly lawyer to act as his Agent. After signing the document, the man is involved in a serious car accident and enters a long coma. After a year, the lawyer retires and indicates that he is no longer willing to perform his duties as Agent. If the man appointed a Successor Agent in his contract, the new Agent will now assume responsibility for the man's legal and financial concerns.