Rare animals have an important and vital role to play in the ecosystem. They should be preserved even if no other reason than so that other generations can see them and learn a about these rare species from something other than history books or a photograph and videos on the internet.
Animals should be saved and preserved. If we have found one elephant, we could save it, find a second, breed it and then re-release. If it is alone, rare, small, it could be poached, killed or sold for it's rarity. We deserve to protect it and conserve it so that hopefully future generations can see the elephant.
If the species is rare because they have been hunted to humans or had their habitat irrevocably damaged, what remains of those species should be preserved. If natural selection, evolution or changes in climate are to blame, let the weak species go extinct. We aren't really capable of managing our own species, let alone playing God to the rest of the natural world.
We are running out of lot of species of animals due to human encroachment on the wild lands. If this kind of human development keeps taking over the nature, the balance of nature is going to lose which will cause a lot of natural calamities. Preserving rare species will help us learn more about out planet and causes of extinction. This will in turn help us make our world more sustainable.