Wireless technology enables novel approaches to healthcare, in particular the remote monitoring of vital signs and other parameters indicative of people's health. This paper considers a system scenario relevant to such applications, where a smart-phone acts as a data-collecting hub, gathering data from a number of wireless-capable body sensors, and relaying them to a healthcare provider host through standard existing cellular networks. Delay of critical data and sensors' energy efficiency are both relevant and conflicting issues. Therefore, it is important to operate the wireless body-area sensor network at some desired point close to the optimal energy-delay tradeoff curve. This tradeoff curve is a function of the employed physical-layer protocol: in particular, it depends on the multiple-access scheme and on the coding and modulation schemes available. In this work, we consider a protocol closely inspired by the widely-used Bluetooth standard. First, we consider the calculation of the minimum energy function, i.e., the minimum sum energy per symbol that guarantees the stability of all transmission queues in the network. Then, we apply the general theory developed by Neely to develop a dynamic scheduling policy that approaches the optimal energy-delay tradeoff for the network at hand. Finally, we examine the queue dynamics and propose a novel policy that adaptively switches between connected and disconnected (sleeping) modes. We demonstrate that the proposed policy can achieve significant gains in the realistic case where the control "NULL" packets necessary to maintain the connection alive, have a non-zero energy cost, and the data arrival statistics corresponding to the sensed physical process are bursty.