For the classical Shiryaev–Roberts martingale diffusion considered on the interval $[0, A]$, where $A > 0$ is a given absorbing boundary, it is shown that the rate of convergence of the diffusion’s quasi-stationary cumulative distribution function (cdf), $Q_A(x)$, to its stationary cdf, $H(x)$, as $A$ goes to infinity, is no worse than $O(\log(A)/A)$, uniformly for any $x\ge0$.