© 2021 IEEE.Underwater wireless sensor networks (UWSNs) are, typically, comprised of sparsely deployed sensor nodes in hostile areas. Security of data flows among nodes are established by encryption of data packets, however, due to the limited memory of the sensor nodes, only a subset of keys distributed to the whole network exists at each node, therefore, only a subset of available physical links can be used for secure communications. Indeed, two neighbor sensor nodes can establish secure connectivity only if they share a common key, therefore, the existence of a physical link between a node pair is not sufficient to establish direct secure communications if they do not share a common key. Incomplete secure connectivity makes UWSNs more vulnerable to critical node failures because of the reduction in alternative paths towards the base station. In fact, it is possible to reduce the network lifetime of UWSNs significantly by incapacitating the most critical node in a given deployment topology, which is exacerbated by incomplete secure connectivity. Such nodes, typically, are found in close proximity to the base station. In this study, a linear programming (LP) model is developed to explore the effects of critical node failures on the lifetime of UWSNs with incomplete secure connectivity. Our results reveal that critical node incapacitation can reduce the network lifetimes by up to 47% while increasing the energy consumption overhead of the network by up to 46%.