In this work, Wireless Sensor Network (WSN) applications that require long-term sustainability are considered. Energy harvesting forms a promising technology to address this challenge, by allowing each node to be entirely powered by energy harvested from its environment. To be sustainable, each node must dynamically adapt its Quality of Service (QoS), regarding the harvested energy using a power management strategy. This strategy is implemented on each node by the Power Manager (PM). In this paper, GRAPMAN (GRAdual Power MANager) is proposed, a novel PM for Energy-Harvesting WSN (EH-WSN) powered by pseudo-periodic energy sources. Unlike most state of the art PMs, GRAPMAN aims to achieve high average throughput while maintaining consistent QoS, i.e. with low fluctuations with respect to time, by looking for the highest throughput that can be supplied by the node over a finite time horizon while remaining sustainable. We show through extensive trace-driven network simulations that GRAPMAN outperforms state of the art PMs in both average throughput and throughput consistency.