Does a power of attorney stay in effect after the person who granted it dies?

No. A power of attorney, durable or not, automatically ends the moment the person who granted it dies. At that point the agent has no further authority, and control passes to the executor named in the will or the successor trustee of a trust. This surprises many families who assume the agent can keep paying bills or distributing assets after death; doing so would be acting without legal authority. The agent's job is strictly to manage affairs during your lifetime, especially incapacity. After death, the estate must be administered through probate or the trust process. This is why you need both a durable power of attorney for your lifetime and a will or trust to govern what happens after.