The decay of the nuclear magnetization along a spin-locking field in the rotating frame has been studied in solid deuterium, at a frequency of 4.7 MHz, following the method of Rowland and Fradin. Measurements were made between 4 and 13 K, on samples having para (J=1) mole fractions X ranging from 0.04 to 0.9. The lab-frame transverse relaxation time T2 was measured in the range 13-17 K. These data permitted the observation of thermally activated diffusion between 9 and 17 K, corresponding to a change in the characteristic time τ between molecular jumps of some seven orders of magnitude. The activation energy is (276 ± 20) K, independent of concentration. No evidence could be detected of the slow diffusion from quantum tunneling of vacancies predicted by Ebner and Sung. For the temperature range below about 8 K, the rotating-frame formalism has been adapted to the specific spin-lattice relaxation mechanisms present in D2, and account has been taken of the intramolecular spin-spin interactions. Effects of translational molecular motion were not seen in this region. This is consistent with the very slow rates expected theoretically by Oyarzun and Van Kranendonk. At intermediate and high (J=1) mole fractions X and below about 8 K, the exponential decay of the spin-locked magnetization was preceded by a short transient of approximately 0.1-sec duration. This transient is thought to be associated with the internal equilibration of the nuclear-spin energy systems. Its lifetime Tx is much longer than T2 of the rigid lattice because the NMR line is inhomogeneously broadened by the intramolecular spin-spin interactions. The magnitude of Tx has been correlated with previously reported cross-relaxation times for the lab frame.