A knowledge of stellar ages is crucial for our understanding of many astrophysical phenomena, and yet ages can be difficult to determine. As they become older, stars lose mass and angular momentum, resulting in an observed slowdown in surface rotation1. The technique of ‘gyrochronology’ uses the rotation period of a star to calculate its age2, 3. However, stars of known age must be used for calibration, and, until recently, the approach was untested for old stars (older than 1 gigayear, Gyr). Rotation periods are now known for stars in an open cluster of intermediate age4 (NGC 6819; 2.5 Gyr old), and for old field stars whose ages have been determined with asteroseismology5, 6. The data for the cluster agree with previous period–age relations4, but these relations fail to describe the asteroseismic sample7. Here we report stellar evolutionary modelling5, 6, 8, 9, 10, and confirm the presence of unexpectedly rapid rotation in stars that are more evolved than the Sun. We demonstrate that models that incorporate dramatically weakened magnetic braking for old stars can—unlike existing models—reproduce both the asteroseismic and the cluster data. Our findings might suggest a fundamental change in the nature of ageing stellar dynamos, with the Sun being close to the critical transition to much weaker magnetized winds. This weakened braking limits the diagnostic power of gyrochronology for those stars that are more than halfway through their main-sequence lifetimes.