How can one relinquish his authority under a Power of Attorney?

First let me point out that even though one is the agent pursuant to a Power of Attorney, she does not have to act pursuant to its authority.  However, no one else can have Power of Attorney as long as she does and it would be unethical for to refuse to act if necessary.  The legal way to relinquish your responsibilities is to file a Revocation of the Power of Attorney signed by the giver of the Power.  Alternatively, that person can file a new POA naming someone else and this would automatically revoke the original agent.  Either way, the document has to be signed, notarized and filed in the same Register of Deeds office where the original Power of Attorney was filed.  It is best to have an attorney prepare this document so that you are sure it accomplishes the revocation.  Then, someone else can be appointed by a new Power of Attorney.