Organic solar cells that are free of burn-in, the commonly observed rapid performance loss under light, are presented. The solar cells are based on poly(3-hexylthiophene) (P3HT) with varying molecular weights and a nonfullerene acceptor (rhodanine-benzothiadiazole-coupled indacenodithiophene, IDTBR) and are fabricated in air. P3HT:IDTBR solar cells light-soaked over the course of 2000 h lose about 5% of power conversion efficiency (PCE), in stark contrast to [6,6]-Phenyl C61 butyric acid methyl ester (PCBM)-based solar cells whose PCE shows a burn-in that extends over several hundreds of hours and levels off at a loss of ≈34%. Replacing PCBM with IDTBR prevents short-circuit current losses due to fullerene dimerization and inhibits disorder-induced open-circuit voltage losses, indicating a very robust device operation that is insensitive to defect states. Small losses in fill factor over time are proposed to originate from polymer or interface defects. Finally, the combination of enhanced efficiency and stability in P3HT:IDTBR increases the lifetime energy yield by more than a factor of 10 when compared with the same type of devices using a fullerene-based acceptor instead.