In a scenario where sea levels rise, and it is surrounded by sand which is then compressed into sedimentary rock which carries it around "nominally" intact I would guess it survives for quite a while. Of course there isn't anything that says we can't create some tungsten spheres as containers to hold memorabilia from the current time. Even if recycled they would not be destroyed. Of course their interiors would get hot too so you're probably want to have your information etched on thin sheets of tungsten insider the sphere.