Differences between individuals in the rate of food acquisition are conventionally attributed to varying competencies  even though food encounter rates are known to be probabilistic [2, 3]. We used animal-attached technology to quantify food intake in four disparate free-living vertebrates (condors, cheetahs, penguins and sheep) and found that inter-individual variability depended critically on the probability of food encounter. We modelled this to reveal that animals taking rarer food, such as apex predators and scavengers, are particularly susceptible to breeding failure because this variability results in larger proportions of the population failing to accrue the necessary resources for their young before they starve, and because even small changes in food abundance can affect this variability disproportionately. A test of our model on wild animals explained why Magellanic penguins have a stable population while the congeneric African penguin population has declined for decades. We suggest that such models predicting probabilistic ruin can help predict the fortunes of species operating under globally changing conditions.