More specifically, they are not genetically programmed to die, unlike humans or animals for which there is a molecular program provided for this purpose: the genes are extinguished by a biochemical mechanism which is at the origin of the aging.
The growth of trees is infinite in theory, if they are kept in a favorable environment, just like crocodiles and lobsters in the animal world. They also have a very good ability to regenerate their cells, which allows them to reactivate their genes “off” after stopping their growth during periods of extreme cold. Their roots are also of great help: clones of long dead trees can be re-formed by vegetative propagation mechanisms at ground level.
On the other hand, the more the time passes, the more they will have difficulty to heal wounds inflicted by the external agents: the animals and insects, the wind, a fatal illness or an accident (lightning, frost …) and the variations of the climate.