  We revisit here the problem of the collective non-equilibrium dynamics of a
classical statistical system at a critical point and in the presence of
surfaces. The effects of breaking separately space- and time-translational
invariance are well understood, hence we focus here on the emergence of a
non-trivial interplay between them. For this purpose, we consider a
semi-infinite model with $O(n)$-symmetry and purely dissipative dynamics which
is prepared in a disordered state and then suddenly quenched to its critical
temperature. We determine the short-distance behaviour of its response function
within a perturbative approach which does not rely on any a priori assumption
on the scaling form of this quantity.
