Wireless Sensor Networks (WSNs) are deployed in a variety of topologies and configurations depending on specific applications and requirements. In this paper, we study a simple and yet very important class of the WSN topologies, the linear or chain topology in which the Sensor Nodes (SNs) are connected in a series and gather the sensed data at a single base station or sink at the end of the chain. WSNs with linear topology have many practical applications, e.g., in infrastructure monitoring and surveillance of civil constructions. There is a large body of research on efficient data gathering techniques to transmit the sensed data over WSNs' limited communication bandwidth. In particular for linear topology, data collection technique has to put a balanced load on all SNs to avoid breakage of the chain at the exhausted nodes. Compressed Sensing (CS) is an efficient data collection technique for WSNs that fulfills these requirements. In a failure-free scenario, CS avoids exhausted nodes by balancing the communication and processing load on the SNs. In this paper, we examine the performance of a special implementation of CS for WSNs, called Compressive Data Gathering (CDG) when a SN in a chain WSN encounters a failure and cannot forward messages to the next hop. We propose a method to enhance the robustness of CDG in such failure scenarios by transmitting the messages to the next healthy node and excluding the failed samples from CS signal recovery mechanism. Evaluations show that our method effectively withstands the failures without sacrificing the accuracy of the collected data. © 2014 IEEE.