With recent advances in energy harvesting technology, practical wireless nano-sensor networks (WNSNs) are coming within reach. An important aspect of these WNSNs is that the charge time is significantly longer than each sensor mote can reliably transmit its data-leading to sparse transmission requests in the time-domain. In this paper, we propose a compressed sensing-based approach for efficient request handling. We show that our scheme can achieve near contention free transmission while ensuring that each sensor mote's queue is stable. This sharply contrasts with the unstable sensor mote queues obtained using the standard round- robin approach. To guide design, we also derive closed-form expressions for the average energy consumption, which show that the average energy state of the battery increases exponentially with the transmit power.