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Components in many real-world complex systems depend on each other for the resources required for survival, and may die of a shortage. These patterns of dependencies often take the form of a complex network whose structure potentially affects how the resources produced in the system are efficiently shared among its components, which in turn decides a network's survivability. Here we present a simple threshold model that provides insight into this relationship between the network structure and survivability. We show that, as a combined effect of local sharing and finite lifetime of resources, many components in a complex system may die of lack of resources even when sufficient amount is available in the system. We also obtain a surprising result that although the scale-free networks exhibit a significantly higher survivability compared to their homogeneous counterparts, a vertex in the later survives longer on average. Finally, we demonstrate that the system's survivability can be substantially improved by changing the way vertices distribute resources among the neighbours. Our work is a step towards understanding the relationship between intricate resource dependencies present in many real-world complex systems and their survivability.