This paper addresses the problem of maximizing the network lifetime of rechargeable Wireless Sensor Networks (WSNs) whilst ensuring all targets are monitored continuously by at least one sensor node. The objective is to determine a group of sensor nodes, and their wake-up schedule such that within a time interval, one subset of nodes are active whilst others enter the sleep state to conserve energy as well as recharge their battery. We propose a Linear Programming (LP) based solution to determine the activation schedule of sensor nodes whilst affording them recharging opportunities and at the same time ensures complete target coverage. The results show our LP solution achieves more than twice the performance in terms of network lifetime as compared to similar algorithms developed for finite battery WSNs. However, it is computationally expensive. We therefore propose Maximum Utility Algorithm (MUA), a few orders of magnitude faster approach that achieves 3/4 of the network lifetime obtained by our LP solution.