The central eye is a pain for the beholder to use, because if it succeeds with an enchantment, it is tempted to close its central eye from then on for the enchantment to take effect. Meanwhile the rest of the party blasts the poor beholder into oblivion.
Edit: Regarding Blinky's last move, he cannot close his central eye and re-open it in the same round, so I don't think the sleep ray will have any effect.