The $\ensuremath{\Lambda}\ensuremath{\Lambda}$ bond energy $\ensuremath{\Delta}{B}_{\ensuremath{\Lambda}\ensuremath{\Lambda}}$ in $\ensuremath{\Lambda}\ensuremath{\Lambda}$ hypernuclei is obtained from a $G$-matrix calculation which includes the coupling between the $\ensuremath{\Lambda}\ensuremath{\Lambda}$, $\ensuremath{\Xi}N$, and $\ensuremath{\Sigma}\ensuremath{\Sigma}$ channels, as well as the effect of Pauli blocking to all orders. The Nijmegen NSC97e model is used as bare baryon-baryon interaction in the strangeness $S=\ensuremath{-}2$ sector. The $\ensuremath{\Lambda}\ensuremath{\Lambda}$-$\ensuremath{\Xi}N$ coupling increases substantially the bond energy with respect to the uncoupled $\ensuremath{\Lambda}\ensuremath{\Lambda}$ case. However, the additional incorporation of the $\ensuremath{\Sigma}\ensuremath{\Sigma}$ channel, which couples simultaneously to $\ensuremath{\Lambda}\ensuremath{\Lambda}$ and $\ensuremath{\Xi}N$ states, has a surprisingly drastic effect and reduces the bond energy down to a value closer to that obtained in an uncoupled calculation. We find that a complete treatment of Pauli blocking reduces the repulsive effect on the bond energy to about half of what was claimed before.