Leigh Van Valen famously stated that under constant conditions extinction probability is independent of species age. To test this 'law of constant extinction', we developed a new method using deep learning to infer age-dependent extinction and analysed 450 myr of marine life across 21 invertebrate clades. We show that extinction rate significantly decreases with age in > 90% of the cases, indicating that most species died out soon after their appearance while those which survived experienced ever decreasing extinction risk. This age-dependent extinction pattern is stronger towards the Equator and holds true when the potential effects of mass extinctions and taxonomic inflation are accounted for. These results suggest that the effect of biological interactions on age-dependent extinction rate is more intense towards the tropics. We propose that the latitudinal diversity gradient and selection at the species level account for this exceptional, yet little recognised, macroevolutionary and macroecological pattern.