Numerous animals move vast distances through media with stochastic dynamic properties. Avian migrants must cope with variable wind speeds and directions en route, which potentially jeopardize fine-tuned migration routes and itineraries. We show how unpredictable winds affect flight times and the use of an intermediate staging site by red knots (Calidris canutus canutus) migrating from west Africa to the central north Siberian breeding areas via the German Wadden Sea. A dynamic migration model incorporating wind conditions during flight shows that flight durations between Mauritania and the Wadden Sea vary between 2 and 8 days. The number of birds counted at the only known intermediate staging site on the French Atlantic coast was strongly positively correlated with simulated flight times. In addition, particularly light-weight birds occurred at this location. These independent results support the idea that stochastic wind conditions are the main driver of the use of this intermediate stopover site as an emergency staging area. Because of the ubiquity of stochastically varying media, we expect such emergency habitats to exist in many other migratory systems, both airborne and oceanic. Our model provides a tool to quantify the effect of winds and currents en route.