The origin of life remains a scientific mystery, particularly the emergence of protocells. One hypothesis proposes that protocells arose as droplets formed via liquid–liquid phase separation of polymers. The work on this hypothesis leaves open how protocells survived in fluctuating or cyclic environments. We consider a model system incorporating both spontaneous polymerization and droplet-facilitated fuel-driven polymerization. We show that the resulting droplets display a stationary hysteresis with respect to available fuel. Droplets can remain stable even after the fuel-driven polymerization reactions significantly diminish, suggesting a potential mechanism for protocell formation and resilience to environmental fluctuations. This robustness would have enabled protocells to endure early environmental challenges, such as energy shortages in a famine.