ABSTRACT Protoplanetary discs (PPDs) in the Orion Nebula Cluster (ONC) are irradiated by UV fields from the massive star θ1C. This drives thermal winds, inducing mass-loss rates of up to $\dot{M}_\mathrm{wind}∼ 10^{-7}\, \mathrm{M}_⊙$ yr−1 in the ‘proplyds’ (ionized PPDs) close to the centre. For the mean age of the ONC and reasonable initial PPD masses, such mass-loss rates imply that discs should have been dispersed. However, $∼ 80{\,{\rm {per\, cent}}}$ of stars still exhibit a near-infrared excess, suggesting that significant circumstellar mass remains. This ‘proplyd lifetime problem’ has persisted since the discovery of photoevaporating discs in the core of the ONC by O’Dell & Wen (1994). In this work, we demonstrate how an extended period of star formation can solve this problem. Coupling N-body calculations and a viscous disc evolution model, we obtain high disc fractions at the present day. This is partly due to the migration of older stars outwards, and younger stars inwards such that the most strongly irradiated PPDs are also the youngest. We show how the disc mass distribution can be used to test the recent claims in the literature for multiple stellar populations in the ONC. Our model also explains the recent finding that host mass and PPD mass are only weakly correlated, in contrast with other regions of similar age. We conclude that the status of the ONC as the archetype for understanding the influence of environment on planet formation is undeserved; the complex star formation history (involving star formation episodes within ∼0.8 Myr of the present day) results in confusing signatures in the PPD population.