This is a quite interesting question. Without looking up the procedure in Williamson, I recall that everything was added at once in their procedure. However, experience reveals that unless the NaOH is fresh, the reaction can easily fail. In that case, adding additional NaOH(s) will start the reaction again.
Because the reaction only requires a catalytic amount of base as base is regenerated, I think the success of this reaction is related to rates. If small amounts of concentrated base were used, then product formation would dilute the base and slow the reaction. Addition of base could increase the concentration and increase the reaction rate.