This usually happens when the Music Genre your character plays changes. Check your Tama's favorite Music Type. Is it different from what it was when the ranking was 1st?
Make sure they keep practicing, and not playing with their toys. If it goes down you can also go practice with the band. Make sure you're playing games and not feeding snacks.
Make sure that you're catching all three concerts, because those are really important to the ranking.
If you're doing all that it should steadily go up.
Play more often in music city, and keep raising those skill points!!!! Trust me, the more skill points you have, the better your ranking will be, and the more likely you are to get an award will rise
Rankings are a bit crazy. They can go up and down a lot. Like others have said, don't let it play too much and praise it when it practices to keep the stress level down.