What causes a tree, although still living, to eventually stop growing taller?

Some people do believe that hydraulic limitations play a part in limiting growth of the tallest trees, but otherwise it's in the genes, just like tall and not so tall people.

it gets old, just like every other living thing, gets gradually weaker. and of course in cold seasons it remains somewhat dormant. Otherwise, it's continuously trying to keep growing more and more, though you might not notice it or it might not be that much.

It hits puberty, in the same way that when you grow up you'll stop growing, without stopping being alive