We summarize how the approach to the black-disk regime (BDR) of strong interactions at TeV energies influences rapidity gap survival in exclusive hard diffraction pp -> p + H + p (H = dijet, Qbar-Q, Higgs). Employing a recently developed partonic description of such processes, we discuss (a) the suppression of diffraction at small impact parameters by soft spectator interactions in the BDR; (b) further suppression by inelastic interactions of hard spectator partons in the BDR; (c) correlations between hard and soft interactions. Hard spectator interactions substantially reduce the rapidity gap survival probability at LHC energies compared to previously reported estimates.