Except language changes even during human lifetimes. And one of the primary reasons for that is the birth of new generations, which bring differing perspectives.

While the Elves are immortal, they are not sterile. They don't mutliply at human rates, but given their immortality, that would make perfect sense. Their language would, thus, evolve. Just slower than human languages.

And that matches what we see in the books. It takes thousands of years for Elven languages to diverge.