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The sustainability of biological, social, economic and ecological communities is often determined by the outcome of social conflicts between cooperative and selfish individuals (cheaters). Cheaters avoid the cost of contributing to the community and can occasionally spread in the population leading to the complete collapse of cooperation. Although such collapse often unfolds unexpectedly, it is unclear whether one can detect the risk of cheater’s invasions and loss of cooperation in an evolving community. Here, we combine dynamical networks and evolutionary game theory to study the abrupt loss of cooperation with tools for studying critical transitions. We estimate the risk of cooperation collapse following the introduction of a single cheater under gradually changing conditions. We observe an increase in the average time it takes for cheaters to be eliminated from the community as the risk of collapse increases. We argue that such slow system response resembles slowing down in recovery rates prior to a critical transition. In addition, we show how changes in community structure reflect the risk of cooperation collapse. We find that these changes strongly depend on the mechanism that governs how cheaters evolve in the community. Our results highlight novel directions for detecting abrupt transitions in evolving networks.