We develop a model that reveals the preservation value of maintaining connectivity within a socio-ecological system (SES). By means of a multiplex network, built from the layers composing the sustainability Venn diagram, we define two measures of preservation value of inter- and intra-layer connections. Most policymakers and researchers have tended to assume that all elements within an SES are unconditionally connected, which implied that dimensions of sustainability functioned unhindered. We must instead explicitly explore how connectivity is operational. Given explicit threats to connectivity, we show under which conditions connectivity is valuable and should be preserved. This implies that policies aimed at sustainability should focus on explicitly addressing connections and disconnections. Using numerical simulations, our results suggest that the preservation value of the SES topological structure is greatest when we secure the connectivity of inter-layer connections.