Why does spin-spin relaxation not restore the overall equilibrium distribution of nuclear spins?

Spin-spin relaxation does not restore the overall equilibrium distribution of nuclear spins because it involves a process of energy exchange between individual nuclei rather than a dissipation of energy to the surrounding environment.1

In this process, an excited nucleus in an upper spin state transfers its energy to a nearby nucleus that is in a lower spin state. While this exchange shortens the lifetime of the individual excited nucleus, the total number of nuclei in the upper and lower spin states remains unchanged. Consequently, the system does not return to its equilibrium distribution of parallel and antiparallel spins.1

In contrast, spin-lattice relaxation is the process responsible for restoring equilibrium, as it involves the transfer of excess energy from the excited nuclei to the surrounding molecules—the "lattice"—as translational, rotational, or vibrational energy.1