There are certain annual(eg.peas) and biennial plants(eg.carrot) also which die at fixed times.
But for perennial plants :
Trees endure as long as they do basically because they're
nonhierarchical organisms. In animals, all vital functions are
controlled by the central nervous system, the guiding element of which
is the brain. When the brain dies, so does the animal. By contrast,
vital functions in trees are decentralized. A large part of the tree
can die, and indeed routinely does die, without killing off the tree
as a whole. Most of a mature tree is dead except for a few layers
under the bark.....
All trees die eventually, of course. Four thousand years is old
compared to the life spans of gossamer creatures like ourselves, but
in the context of geologic time it's the blink of an eye. As they get
older trees become more susceptible to disease, pests, and other
perils, and inevitably these take their toll.