Amid global pandemics and climate change, it is clear that coupled models of human and environmental systems are needed. These socio-ecological models have been used to understand fisheries, disease spread, and deforestation. These models have only recently been used to understand how human actions and behavior affect coral reef fisheries, with a focus on shifts to alternative stable states. We extend this work to study the effect of catastrophes, e.g. hurricanes, on these systems. We show the conditions necessary for long-term coral reef health with fishing. We also examine the effect of the disturbance regime (timing, magnitude, type) on the overall system dynamics. These results both advance our understanding of catastrophes and socio-ecological systems as well as point to ways to build fisheries that are robust to rare events.