Wireless Body Area Networks (WBANs) refer to a class of wireless sensor networks that are expected to support a wide variety of applications ranging from healthcare and emergency response to entertainment and sports. A WBAN can be characterized by a small number of heterogeneous sensors and an energy-constrained fusion center e.g. cellphone. A key goal is to maximize the lifetime of such a unique sensor network and based on an actual implementation of a prototype WBAN, the limited energy budget of the fusion center is a critical impediment. To overcome this issue, the stochastic control framework introduced in our earlier work is extended to account for less number of samples and sensor heterogeneity is redefined in terms of worst-case detection error probability. A Maximum Likelihood detector based on the belief state is also introduced to increase the detection performance. To account for the energy-constrained fusion center, our initial optimization problem is reformulated to two alternative, but distinct constrained versions and two completely new algorithms, E²MBADP and GME²PS², are devised. Simulations on real-world data are provided to validate the schemes' performance. Energy gains on the order of 64% while achieving the same detection accuracy (99%) as an equal allocation scheme across sensors are observed.