We have studied the coherent spin dynamics of excitons bound to acceptors, A0X, immersed in a CdTequantum well by using time resolved photo-induced Faraday rotation. We have also measured the time-resolved differential transmission in order to determine a A0X lifetime of 220 ps, which is independent of the applied magnetic field. We show that at low magnetic field, the spin of A0X is completely frozen during a time, ≅ 4.5 ns, at least twenty times longer than its lifetime. We compare the spin properties of A0X with the spin properties of other charged excitons systems, and we conclude that the hyperfine interaction of the photo-created electron spin with nuclear spins is very likely to be at the origin of the observed spin dephasing times.