For many decades, frictional strength increase at low slip rates has been ascribed to time-dependent contact-area growth across the sliding interface. As a result, phenomenological models that correctly predict contact-area growth, as observed in laboratory experiments, have also been widely assumed to be appropriate descriptors of frictional strength evolution. We present experiments that impose more than 5-orders-of-magnitude slip-rate reductions on granite to show that frictional strength evolution in these rocks unequivocally refutes such models. Instead, the data suggest that, even at subnanometric slip rates, frictional strength dominantly evolves with accrued slip. This remarkable slip-sensitivity of friction requires changes of intrinsic strength of the interface with slip that are absent from popular conceptual models of friction at the microscopic contact scale.