The production of electron-positron pairs with subsequent inner-shell capture of the produced electron in relativistic collisions of heavy ions has recently been investigated within a coupled-channel formalism based on an expansion in atomic orbitals of the target. At close collisions a drastic failure of perturbation theory in first order has been found. For the case of the collision of U92+ + U92+ at an incident energy of 2 GeV/nucleon we demonstrate, that this non-perturbative behaviour is essentially due to the strong interaction of the K-shell bound state with the field of the projectile charge.