Energy harvesting wireless sensor network (EH-WSN) is promising in applications, however the frequent occurrence of temporal death of nodes, due to the limited harvesting capability, presents a difficulty in meeting the quality-of-service requirements of the network. For a node with temporal death in an EH-WSN, this paper presents a new model, which consists of, a Markov model to trace the energy harvesting process, a queuing analytical model to model the working mechanism of the sensor node and a continuous fluid process to capture the evolution of the residual energy in the EH-WSN node. Using the Markov fluid queue (MFQ) theory, we discuss various performance aspects of the EH-WSN node with temporal death, including the temporal death occurrence probability, the probability density of the residual energy, the stationary energy consumption, the queue length distribution in the data buffer, the packet blocking probability, and so on. In order to obtain the dropping probability of a given packet, based on the structure of the MFQ, we develop an auxiliary MFQ and derive the formulations of two types of the packet dropping probabilities, i.e., the packet dropping probability due to energy depletion and that due to channel error. Numerical examples are provided to illustrate the theoretical findings, and new insights into understanding the impacts of the parameters on the performance metrics are presented.