Wireless sensor networks are used in many environmental monitoring applications (e.g., to monitor forest fires or volcanoes). In such applications, sensor nodes have a limited quantity of energy, but must operate for years without having their batteries changed. The main mechanism used to allow nodes to save energy is to sequence periods of activity and inactivity. However, the design of MAC and routing protocols for applications with low duty-cycle is still a challenge. In this paper, we propose an efficient flooding-based protocol combined with an unsynchronized MAC protocol operating at very low duty-cycle (≤ 1%) called E-ADCR (Energy-efficient Asynchronous low Duty-Cycle Routing protocol). Although flooding-based routing protocols are usually very simple to implement, they are often costly in terms of bandwidth, due to the large number of data copies. Our flooding-based routing protocol has the following features: (i) it benefits from rare common activities to reduce the amount of data copies generated by the flooding mechanism, (ii) it guarantees the reception of frames by a limited number of receivers by sending frames multiple times during the active period, and (iii) it uses a queue management policy to ensure that frames do not stay to long in queues. With these features and the strong cross-layer design with the MAC protocol, our protocol is able to achieve good performance with this very low duty-cycle.