The paper discusses a large class of backward stochastic Volterra integral equations whose coefficients additively depend on small perturbations. Their solutions are compared in the L^2-sense, with the solutions of the appropriate unperturbed equations of the equal type. We prove that for an arbitrary η >0 there exists an interval [͞t(η),T] subset of [0,T] on which the L^2-difference between the solutions of perturbed and unperturbed equations is less than η. In contrast to similar problems about various perturbed forward and also backward stochastic differential equations, a completely different procedure must be applied on perturbed backward stochastic Volterra integral equations.