  We investigate the longitudinal spin relaxation arising due to spin-flip
transitions accompanied by phonon emission in quantum dots where the strength
of the Rashba spin-orbit coupling is a random function of the lateral
(in-plane) coordinate on the spatial nanoscale. In this case the Rashba
contribution to the spin-orbit coupling cannot be completely removed by
applying a uniform external bias across the quantum dot plane. Due to the
remnant random contribution, the spin relaxation rate cannot be decreased by
more than two orders of magnitude even when the external bias fully compensates
the regular part of the spin-orbit coupling.
