There is a need for sensing technologies that can continuously monitor concentration levels of critical biomolecules in applications such as patient care, fundamental biological research, biotechnology and food industry, as well as the environment. However, it is fundamentally difficult to develop measurement technologies that are not only sensitive and specific, but also allow monitoring over a broad concentration range and over long timespans. Here we describe a continuous biomolecular sensing methodology based on the free diffusion of biofunctionalized particles hovering over a sensor surface. The method records digital events due to single-molecule interactions and enables biomarker monitoring at picomolar to micromolar concentrations without consuming any reagents. We demonstrate the affinity-based sensing methodology for DNA-based sandwich and competition assays, and for an antibody-based cortisol assay. Additionally, the sensor can be dried, facilitating storage over weeks while maintaining its sensitivity. We foresee that this will enable the development of continuous monitoring sensors for applications in fundamental research, for studies on organs on a chip, for the monitoring of patients in critical care, and for the monitoring of industrial processes and bioreactors as well as ecological systems.