I tied my java moss to driftwood in my tank with fishing line and two days later I cut the line and it has rooted and stayed there since. The few loose strands I do have find the bottom and stay there with the fish moving them around and they eventually attached themselves to something else in the tank and start growing.
If your fish are "kicking" them up then tied them down. Or perhaps you have too much flow in the tank moving it about?
I find Java moss grows quicker when it's in the path of moving water like from your filter or power heads etc... definitely requires tying down though.