The opening and closing of nanocavities in a model soft nanocomposite subjected to cyclic uniaxial tension were directly studied by real-time small-angle X-ray scattering (SAXS). The volume fraction and average shape of the nanocavities have been detected by a pronounced increase in the scattering invariant Q/Q(0) and a detailed analysis of the scattering patterns. Cavities appear upon loading past an intrinsic stress sigma(int) or intrinsic elongation lambda(int). Upon unloading, nanocavities are progressively closed until the volume void fraction phi(void) reaches 0 for a constant "closure stress" of about 3.5 MPa. As the sample is reloaded, no cavities are observed when the current elongation remains below the maximum elongation of previous cycles lambda(max)(N - 1) (N is the number of the cycles). Above this elongation, the void volume fraction phi(void) of the sample increases again. In contrast with phi(void), the cumulative void volume fraction phi(cum_void) appearing in the sample to reach a given maximum historical elongation, lambda(max), or equivalently maximum historical stress sigma(max), was found to be independent of loading history. Both results point toward a process of creation of nanovoids in confined rubber domains that have not previously cavitated rather than to the reopening of the previously created cavities. All critical cavitation parameters display a strong memory effect, mostly captured in this uniaxial test by the maximum historical stress or elongation. The closure stress probably results from the Laplace pressure. A mechanism based on the rearrangement of filler agglomerates by strong shear stress after the emergence of nanocavities is proposed to account for the formation and release of the local geometric confinement and the non-reopening of the previously opened nanovoids upon reloading.