A critical node is a sensor whose failure causes loss of connectivity and network fragmentation. In wireless sensor networks, the failure of a critical node, like the failure of all sensor nodes, can be caused by energy depletion or physical failure. To overcome the problem of failure of such nodes, this article proposes a fault-tolerant strategy that allows a routing protocol to tolerate the failure of a critical node. The proposed strategy is carried out in two phases. In the first phase, a hybrid genetic algorithm with a local search heuristic called genetic algorithm-critical node problem (GA-CNP) is used to select the critical nodes and in the second phase, an algorithm called Aug-CNP is involved to deal with the augmentation problem by deploying additional wireless edges to preserve network connectivity in case of critical node failure. Our proposal has been developed using the OMNET++ simulator, evaluated, and compared to the AODV protocol. The simulation results showed that the GA-CNP algorithm selects the critical nodes whose failure can degrade the network lifetime with a rate of 40%. Moreover, the Aug-CNP algorithm applied to the AODV protocol brings improvements in terms of network lifetime which reaches 22% compared to the traditional AODV protocol.