The deep extension of the San Andreas Fault is believed to be creeping, but the recent observations of tectonic tremors from these depths indicate a complex deformation style. In particular, an isolated tremor source near Parkfield has been producing a sequence of low-frequency earthquakes that indicates an uncommon mechanism of stress accumulation and release. The tremor pattern regularly oscillated between three and six days from mid-2003 until it was disrupted by the 2004 magnitude 6.0 Parkfield earthquake. After that event, the tremor source ruptured only about every three days, but over the next two years it gradually returned to its initial alternating recurrence pattern. The mechanism that drives this recurrence pattern is unknown. Here we use physics-based models to show that the same tremor asperity--the region from which the low-frequency earthquakes radiate--can regularly slip in slow and fast ruptures, naturally resulting in recurrence intervals alternating between three and six days. This unusual slip behaviour occurs when the tremor asperity size is close to the critical nucleation size of earthquakes. We also show that changes in pore pressure following the Parkfield earthquake can explain the sudden change and gradual recovery of the recurrence intervals. Our findings suggest a framework for fault deformation in which the same asperity can release tectonic stress through both slow and fast ruptures.