Energy-harvesting devices have enabled Internet of Things applications that were impossible before. One core challenge of batteryless sensors that operate intermittently is reliable timekeeping. State-of-the-art low-power real-time clocks suffer from long start-up times (order of seconds) and have low timekeeping granularity (tens of milliseconds at best), often not matching timing requirements of devices that experience numerous power outages per second. Our key insight is that time can be inferred by measuring alternative physical phenomena, like the discharge of a simple RC circuit, and that timekeeping energy cost and accuracy can be modulated depending on the run-time requirements. We achieve these goals with a multi-tier timekeeping architecture, named Cascaded Hierarchical Remanence Timekeeper (CHRT), featuring an array of different RC circuits to be used for dynamic timekeeping requirements. The CHRT and its accompanying software interface are embedded into a fresh batteryless wireless sensing platform, called Botoks, capable of tracking time across power failures. Low start-up time (max 5 ms), high resolution (up to 1 ms) and run-time reconfigurability are the key features of our timekeeping platform. We developed two time-sensitive batteryless applications to demonstrate the approach: a bicycle analytics tool, where the CHRT is used to track time between revolutions of a bicycle wheel, and wireless communication, where the CHRT enables radio synchronization between two intermittently-powered sensors.