This paper presents a theoretical investigation of nuclear spin-lattice relaxation time in epitaxial layers of GaAs doped by Mn ions (the concentration of the deep acceptor Mn 3∙1017 cm−3) under optical pumping conditions at the  lattice temperature of 4.5 K. Earlier experiments by the optical orientation method showed that the spin-lattice relaxation time depends on the magnitude of the external magnetic field and reaches up to 20 seconds for this sample.  Such behavior is not typical for p-type semiconductors and is more similar to the nuclear spin system dynamics in n-type GaAs. To determine the reasons for the significant difference in the spin-lattice relaxation time between p-GaAs  and GaAs:Mn, the influence of two possible nuclear spin relaxation mechanisms specific to this material has been evaluated. It is demonstrated that the nuclear spin-lattice relaxation under the action of fluctuating magnetic fields of paramagnetic Mn centers in GaAs does not play a significant role. Relaxation limited by spin diffusion due to hyperfine interaction with Mn holes localized on deep acceptors can make a noticeable contribution to the relaxation rate.