We study the magnetic-field dependence of the longitudinal spin relaxation time T 1 of donor-bound electrons placed in the middle of an 8-nm CdTe quantum well with different doping concentrations in the range from 1 × 10 9 to 2.9 × 10 11 cm −2 and at low temperature. We use an extended photoinduced Faraday rotation technique, which expands the usual domain of the measured decays from tens of ns to μs. As in high-purity bulk semiconductors, a maximum relaxation time of around T 1 ∼ 10 μs is observed for a residually doped sample at low magnetic field of B = 0.08 T. For higher doping concentrations, the magnetic-field dependence of T 1 shows a nonmonotonic behavior: first a rapid increase, followed by a plateau or a decrease of T 1. The fast increase of T 1 at low magnetic fields is explained by the inhibition of the mechanisms identified at zero field-hyperfine and anisotropic exchange interactions-while the behavior at high magnetic field can be succesfully explained by a mechanism proposed by Lyubinskiy and associated to electron hops [I. S. Lyubinskiy, JETP Lett. 88, 814 (2008)]. A good agreement between experiment and theory is found for samples below the metal-insulator transition, when Dresselhaus terms of spin-orbit coupling are considered to be the dominant ones in the Hamiltonian describing the system.