Question: Why did this leaf turn brown and what can I do?
This center leaf problem is something that I faced a lot in the past. I almost eradicated the problem by adding crushed oyster shell to the top of the moss when I repotted. The shells release calcium which is a nutrient particularly important to new growth. You can use a Ca supplement (like Cal-Mag, effective but expensive), crushed egg shell (which you probably already have), or crushed oyster shell (available super cheap anywhere you can get chicken supplies), and that should help the future growths. I used to think that those growths would just die after the center leaf crapped out, but I have since found that to be untrue. At least sometimes, a new center leaf will emerge. At worst, that fan produces no new leaves, but new offshoots will form at its base.