Ultracold atoms are a powerful resource for quantum technologies. As such, they are usually confined in an external potential that often depends on the atomic spin, which may lead to inhomogeneous broadening, phase separation and decoherence. Dynamical decoupling provides an approach to mitigate these effects by applying an external field that induces rapid spin rotations. However, a continuous periodic driving of a generic interacting many-body system eventually heats it up. The question is whether dynamical decoupling can be applied at intermediate times without altering the underlying physics. Here we answer this question affirmatively for a strongly interacting degenerate Fermi gas held in a flat box-like potential. We counteract most of the gravitational force by applying an external magnetic field with an appropriate gradient. Since the magnetic force, and consequently, the whole potential, is spin-dependent, we employ rf to induce a rapid spin rotation. The driving causes atoms in both spin states to experience the same time-average flat potential, leading to a uniform cloud. Most importantly, we find that when the driving frequency is high enough, there is no heating on experimentally relevant timescales, and physical observables are similar to those of a stationary gas. In particular, we measure the pair-condensation fraction of a fermionic superfluid at unitarity and the contact parameter in the BEC-BCS crossover. The condensate fraction exhibits a non-monotonic dependence on the drive frequency and reaches a value higher than its value without driving. The contact agrees with recent theories and calculations for a uniform stationary gas. Our results establish that a strongly-interacting quantum gas can be dynamically decoupled from a spin-dependent potential for long periods of time without modifying its intrinsic many-body behavior.