In this work, we study the convergence dynamics of two independent random configurations of the Bak-Sneppen model of self-organized criticality evolving under the same external noise. A recently proposed measure of the Hamming distance which considers the minimum difference between displaced configurations is used. The displacement evolves in time intermittently. We compute the jump activity rate and waiting time distribution and report on their asymptotic power-law scaling which characterizes the slow relaxation and the absence of typical length and time scales typical of critical dynamical systems. (c) 2006 Elsevier B.V. All rights reserved.