This paper proposes a polynomial-time algorithm for energy-efficient dynamic packet downloading from medical cloud storage to medical Internet-of-Things (IoT) devices. The medical cloud can distribute its own medical data to medical IoT devices via access points. Therefore, network disconnection can happen between the medical cloud and medical IoT devices when power/energy management in each access point is not efficient. This situation is especially harmful in in-hospital network architectures, because the architecture usually has strict requirements in terms of reliability. Therefore, this paper proposes a dynamic energy-efficient algorithm, which computes the amount of power allocation in each access point based on the buffer backlog size and channel states under the consideration of buffer stability. With the proposed adaptive algorithm, each access point calibrates its own parameters for more adaptive power/energy management. The performance of the proposed algorithm is evaluated in terms of network lifetime, and it is observed that the proposed algorithm achieves the desired performance.