Java fern grow better under low lights due to their "slow" growth. Under higher lights you run the risk of green spot algae that tends to take advantage of the plants with slow growth under higher light (like Anubias). Java moss on the other hand are faster growers and will do better with more light....maybe you have the 2 confused? Not to say that java moss won't flourish in low lit tanks, but they tend to do better with more direct light....but I don't think lighting is your problem.
The problem I've noticed with java moss is that it does not compete very well with other plants. If it is the only plant, it does great, but if you add a lot of fast growing plants, it tends to suffer since it gets all it's nutrients from the water rather than the gravel/substrate. Do you add nutrients to the water? Another thing I've seen and read that hinders java moss growth is Excel. This CO2 substitute has been known to kill some types of algae, and seems to slow the growth/and potentially kill mosses as well.