This paper considers a delay tolerant network consisting of nodes equipped with sensors, some of them producing outliers. A distributed faulty node detection (DFD) algorithm, whose aim is to help each node in estimating the status of its sensors, has been proposed recently by the authors. The aim of this paper is to analyze the robustness of the DFD algorithm to the presence of misbehaving nodes performing Byzantine attacks. Two types of attacks are considered and analyzed, each trying to mislead the other nodes in the estimation of the status of their sensors. This provides insights on the way the parameters of the DFD algorithm should be adapted to minimize the impact of misbehaving nodes. Theoretical results are illustrated with simulations considering nodes with random displacements, as well as traces of node inter-contact times from real databases.