Persistence is a quality of most relevance to apple trees and ornamental fruit trees - although it can apply to any type of fruit tree.
In most cases fruit will stay on the tree waiting to be picked, and then gradually start to fall when over-ripe.
Some varieties will drop their fruit before or as it becomes ripe. This can be useful if the fruit is grown for cooking or juicing as it saves picking.
A few varieties ripen their fruit over an extended period, allowing several pickings.
Persistent fruits stay on the tree well into November and December, even January in some cases. This is desirable in crab-apples, as it means the ornamental appeal of the attractive fruit is maintained into winter. Persistent fruits also provide a useful winter food source for wildlife.