For flexibility, you should look more at the structure than at the material choices. With the correct structure, many materials can be tremendously flexible. Also, you need more than flexibility. Many things are flexible, but you need them to be rigid enough to support a load as well, and return to normal afterwards.
Wood can meet your needs:
Properly organized, wood is sufficiently flexible to let palm trees bend out of the way of hurricane force winds.
Steel can meet your needs:
Steel comes in more variants than you can study in a lifetime! Some of them are very rigid and brittle, but others are remarkably flexible.
Glass can be flexible:
Just to show how many materials can meet these needs, with a water cutter one can even cut a glass spring! Even glass flexes when shaped correctly!
What you really care about is structure.
This, of course, is a good thing for you. If materials was the only thing that mattered, you could be in trouble. In general, the ability to flex dramatically and longevity are opposing desires. Most things which flex break down quickly because they have many degrees of freedom. Cross-linked rubber would be amazing for the flexibility requirement you need, but does wear out under UV radiation.
Earthquake proof buildings are constructed with the same steel, glass, and concrete that other buildings are. However, they structure them to be resistant to the particular loads an earthquake can cause. For example, to combat a longitudinal wave, such buildings are often built on giant steel ball bearing-like joints which permit the building to rock back and forth in an earthquake.
One can also take lessons from the ancient Japanese. They designed entire pagodas to flex at many joints to combat earthquakes, as can be seen in the computer simulations below. Nothing was nailed down in these buildings. In fact, many of them were later moved to America, simply by pushing out the wooden pins holding everything together, disassembling the parts, and reassembling them.
These may be of particular interest to you because many of these buildings are hundreds of years old, meeting your durability requirements as well, using nothing but wood and careful construction!