  We investigate the role of the nuclear spin quantum dynamics in
hyperfine-induced spin relaxation of hopping carriers in organic
semiconductors. The fast hopping regime with a small carrier spin precession
during a waiting time between hops is typical for organic semiconductors
possessing long spin coherence times. We consider this regime and focus on a
carrier random walk diffusion in one dimension, where the effect of the nuclear
spin dynamics is expected to be the strongest. Exact numerical simulations of
spin systems with up to 25 nuclear spins are performed using the Suzuki-Trotter
decomposition of evolution operator. Larger nuclear spin systems are modeled
utilizing the spin-coherent state $P$-representation approach developed
earlier. We find that the nuclear spin dynamics strongly influences the carrier
spin relaxation at long times. If the random walk is restricted to a small
area, it leads to the quenching of carrier spin polarization at a non-zero
value at long times. If the random walk is unrestricted, the carrier spin
polarization acquires a long-time tail, decaying as $ 1/\sqrt{t}$. Based on the
numerical results, we devise a simple formula describing the effect
quantitatively.
