The rho rho interaction and the corresponding dynamically generated bound states are revisited. We demonstrate that an improved unitarization method is necessary to study the pole structures of amplitudes outside the near-threshold region. In this work, we extend the study of the covariant rho rho scattering in a unitarized chiral theory to the S-wave interactions for the whole vector-meson nonet. We demonstrate that there are unphysical left-hand cuts in the on-shell factorization approach of the Bethe-Salpeter equation. This is in conflict with the correct analytic behavior and makes the so-obtained poles, corresponding to possible bound states or resonances, unreliable. To avoid this difficulty, we employ the first iterated solution of the N/D method and investigate the possible dynamically generated resonances from vector-vector interactions. A comparison with the results from the nonrelativistic calculation is provided as well.