Actually if you're playing the PS3, on normal, mood changes don't go according to the 360 version. For some weird reason, the penalty's not applied.
A more general case is this - if a particular idol hasn't been happy lately it usually means they haven't had much attention. One way to fix this is to take them out on promotion - it will increase the likelyhood they'll get fanmail.
If you get fanmail, you'll probably increase their mood closer to normal.