What Triggers the Addition of New Balls in 'Relentless' Mode?

It's not random. The process of adding balls to the table is triggered when the number balls remaining falls below a certain threshold (25% I think) and continues for several shots until the the table contains the original number of balls.

If you clear the table quite quickly it's entirely possible to clear it completely at which point the table will be refilled in one go.

The idea was to create some sort of ebb & flow with the table getting quite empty at times an very full at other times. Replacing the balls constantly proved frustrating and far less interesting to play.