People change, new ideas are introduced to them, and this in turn changes the people.

We can't really imagine what it is like to be an immortal / never ending lifespan. But we can make comparisons and inferences with examples of real life humans that have an 80 year old lifespan.

How a person communicates the style of their language changes in their teen years, vs young adults years, vs adulthood. Throw in life events like becoming a parent and your whole world shakes.

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It is hard to see for the change is gradual, but we are talking years in human terms, but remember elves we are talking 4,000 years prior to the first age (the age of the trees), and 590ish years with the First Age when men started waking up and Melkor was doing his nasty stuff with the war of the Similarils.

Even if the speakers are immortal they are fundamentally not the same people with the same points of views over this timeframe. People change, people evolve, and thus our language itself changes over time. To quote another author, "Language is a river, not an ice cube."