We report an experimental approach to excite, stabilize, and continuously track Bloch sphere trajectories of dipolar-coupled nuclear spins in a solid. We demonstrate these capabilities on a model system of hyperpolarized C-13 nuclear spins in diamond. We elucidate a method to drive, and preserve, the motion of spins in complex three-dimensional trajectories for over T '(2)>27s even in the presence of interspin coupling. Indeed, without quantum control, interspin interactions lead to rapid spin decay in T*(2)approximate to 1.5ms. Furthermore, we show that the motion of the spins can be continuously tracked in three dimensions on the Bloch sphere for over 35s. During this time the spins complete >68000 closed precession orbits, exhibiting high stability and robustness against error. Leveraging these long-lived, robust spin trajectories we devise a novel nonequilibrium quantum sensing scheme for DC magnetic fields, based on micromotion dynamics, and without a static counterpart. Sensing here proceeds for the entire T '(2) period, orders of magnitude longer than T*(2), and operates in the dense sensor limit, yielding significant sensitivity improvements. Our results suggest new ways to stabilize and interrogate strongly coupled quantum systems through periodic driving and portend powerful applications of rigid spin orbits in quantum sensing.