We consider theoretically the relaxation of electron spin component parallel to the growth direction in multiple (110) GaAs quantum wells. The sources of spin relaxation are the random Rashba spin-orbit coupling due to the electric field of donors and spin-flip collisions of electrons from different quantum wells. We show that the screening of the Coulomb forces at low temperatures leads to a very strong enhancement of the spin relaxation time. In a degenerate electron gas, the Pauli blocking suppresses the electron-electron collisions, and the leading spin relaxation mechanism comes from the field of donors. If the electron gas is nondegenerate the electron-electron collisions and scattering by the ionized donors give similar contributions to the relaxation rate.