minhag - Why do we wish someone “long life” on the occasion of the anniversary of the death of relative?

Why do english-speaking Orthodox Jews in the UK wish someone “long life” on the occasion of the anniversary of the death of relative?

I can understand this wish directly after the death when I have heard that a person should consider himself as being judged but I find it difficult to understand say 20 years later. I also understand the wish that the soul of the departed should be elevated in the world-to-come.