An agent (also known as an attorney-in-fact) of a New York power of attorney can resign. GOL 5-1505(3) states:
3. Resignation. (a) An agent who has signed the power of attorney may resign by giving written notice to the principal and the agent's co-agent, successor agent or the monitor, if one has been named, or the principal's guardian if one has been appointed. If no co-agent, successor agent, monitor or guardian is known to the agent and the principal is incapacitated or the agent has notice of any facts indicating the principal's incapacity, the agent may give written notice to a government entity having authority to protect the welfare of the principal, or may petition the court to approve the resignation.
(b) The principal may provide for alternative means for an agent's resignation in the power of attorney.
Once the agent resigns, the agent's authority terminates. GOL 5-1511(2)(b) states:
2. An agent's authority terminates when:
. . .
(b) the agent dies, becomes incapacitated or resigns;
Note that the agent's resignation can terminate the power of attorney. GOL 5-1511(1)(e) provides:
1. A power of attorney terminates when:
. . .
(e) the agent dies, becomes incapacitated or resigns and there is no co-agent or successor agent or no co-agent or successor agent who is willing or able to serve;