Children learn language more easily than adults, though when and why this ability declines have been obscure for both empirical reasons (underpowered studies) and conceptual reasons (measuring the ultimate attainment of learners who started at different ages cannot by itself reveal changes in underlying learning ability). We address both limitations with a dataset of unprecedented size (669,498 native and non-native English speakers) and a computational model that estimates the trajectory of underlying learning ability by disentangling current age, age at first exposure, and years of experience. This allows us to provide the first direct estimate of how grammar-learning ability changes with age, finding that it is preserved almost to the crux of adulthood (17.4 years old) and then declines steadily. This finding held not only for "difficult" syntactic phenomena but also for "easy" syntactic phenomena that are normally mastered early in acquisition. The results support the existence of a sharply-defined critical period for language acquisition, but the age of offset is much later than previously speculated. The size of the dataset also provides novel insight into several other outstanding questions in language acquisition.