A cognitive radio sensor network (CRSN) is a wireless sensor network in which sensor nodes are equipped with cognitive radio. CRSNs benefit from cognitive radio capabilities such as dynamic spectrum access and transmission parameters reconfigurability; but cognitive radio also brings additional challenges and leads to higher energy consumption. Motivated to improve the energy efficiency in CRSNs, we propose a robust and energy-efficient transport protocol (RETP). The novelties of RETP are two-fold: (I) it combines distributed channel sensing and channel decision with centralized schedule-based data transmission; and (II) it differentiates the types of data transmission on the basis of data content and adopts different acknowledgment methods for different transmission types. To the best of our knowledge, no transport layer protocols have yet been designed for CRSNs. Simulation results show that the proposed protocol achieves remarkably longer network lifetime and shorter event-detection delay compared to those achieved with a conventional transport protocol, while simultaneously preserving event-detection reliability.