Why does a long bar help a tightrope walker to keep his balance?

The reason simply is the transfer of shifting weight needed to find the equilibrium to counter balance the off-setting side (left of the body vs the right). The body acts as the fulcrum. Hence the longer the bar the slower the transfer time-wise and thus this longer time gives the Tightrope Walker more time in which to react to the constantly changing weight (the adjustments which he uses to stay on the rope: the act of walking constantly changes the weight distribution even fore the best of tightrope walkers).

If the bar were to be too short, the reaction time for the walker would be too quick for him to make the proper adjustments. Also of concern is the weight: too light a bar and not enough weight can be transferred by the walker to adjust and too heavy of a bar and the walker can not hold up the bar (at least not for the time needed to make it across the rope).