Extending the mechanical lifetime of NBR (i.e., poly(acrylonitrile- co-butadiene)), a large-volume synthetic rubber, requires a better understanding of its structure-property relationships. We demonstrate that industrial-grade and uncross-linked NBR can be mechanically rejuvenated and physically aged due to an inhomogeneous distribution of monomers along the polymer chains. As opposed to its nonpolar SBR counterpart (i.e., poly(styrene-co-butadiene)), NBR experiences thermodynamic driving forces for microphase separation and kinetic barriers for processing like those of block copolymers. Extruding NBR at high temperature and shear results in a weakly microphase-separated nanostructure of low relaxation time and resistance to flow, whereas physically aging NBR leads to lamellar nanodomains, a more solid-like material, and delayed stress relaxation. This effect of rejuvenation and aging on the nanostructure and rheological properties of NBR has important consequences on processing and storage conditions, such as the formation of defect-free interfaces in multilayered parts by polymer interdiffusion.