This plant grows by developing the new leaf at one end of the rhizome and this at the same time extends the rhizome in that direction. The older leaves in my experience can remain alive for years. Some 14-15 years ago I had two Anubias plants in my 90g which I had just left alone for six or more years and when I took them out they were just over 24 inches (60 cm) in length.
I've not had any leaves die off yet, I got one plant last September and split it in 3, and have divided it up into about 9 decent size plants now. I think too much light can kill the leaves and the the rhizome should not be covered, but they are pretty much bullet proof.