There is a pine tree that is almost 5,000 years old, and a number of plants "reproduce" by spreading out their root system where what we see as a multitude of plants is essentially one long-lived organism under the surface.

For humans (or at least for me), I think the main concern is really more of continuity of experience than maintaining a particular body configuration indefinitely. I.e. I would like to run into an old friend in 10,000 years and reminisce about that time we did something hilarious. It wouldn't be very satisfying to undergo a procedure that resets my body but wipes out my memories in the process.