We analyze the security vulnerabilities of PEAS, ASCENT, and CCP, three well-known topology maintenance protocols for sensor networks. These protocols aim to increase the lifetime of the sensor network by maintaining only a subset of nodes in an active or awake state. The design of these protocols assumes that the sensor nodes will be deployed in a trusted non-adversarial environment, and does not take into account the impact of attacks launched by malicious insider and outsider nodes. We describe three attacks against these protocols that can be used to reduce the lifetime of the sensor network, or to degrade the functionality of the sensor application by reducing the network connectivity and sensing coverage that can be achieved. Further, we describe counter-measures that can be used to increase the robustness of the protocols and make them resilient to such attacks.