When mooshrooms try to respawn randomly they should check for mycel below them - because that is the thing they live on. But they currently check for grass, that does not even exist on mushroom islands (the only biome mooshrooms can spawn in)..

Reproducing: Kill all mooshrooms on a mushroom island - they will not respawn. Now plant a lot of grass there (replace the mycel by grass) - they will respawn.

This is the check in the decompiled sources, that should probably be overridden for mooshrooms:
https://github.com/Bukkit/mc-dev/blob/master/net/minecraft/server/EntityAnimal.java#L212