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Pervasive health monitoring is an eHealth service, which plays an important role in prevention and early detection of diseases. There are two major challenges in pervasive health monitoring systems with Body Sensor Networks (BSNs). The first challenge is the sustainable power supply for BSNs. The second challenge is Quality of Service (QoS) guarantee for the delivery of data streams. In this paper, we optimize the resource allocations to provide a sustainable and high-quality service in health monitoring systems. Specifically, we formulate and solve two resource optimization problems, respectively. In the first optimization problem, steady-rate optimization problem, we optimize the source rate at each sensor to minimize the rate fluctuation with respect to the average sustainable rate, subject to the requirement of uninterrupted service. The first optimization problem is solved by a proposed analytical solution. The second optimization problem is formulated based on the optimal source rates of the sensors obtained in the steady-rate optimization problem. In the second optimization problem, we jointly optimize the transmission power and the transmission rate at each aggregator to provide QoS guarantee to data delivery. The second optimization problem is converted into a convex optimization problem, which is then solved efficiently. In the simulations, we demonstrate that the proposed optimized scheme enables the pervasive health monitoring system to provide a sustainable service with guaranteed low delay and low Packet Loss Rate (PLR) to subscribers.