The idols that you are "pushing" disappeared when you close the game and then continue the same game save
When you choose three new idols to push, the old three idols you have pushed before you close the game cannot be selected. (The following picture shown that only Momona and Anju's name card can be selected be cause they are either not being pushed now, or not being pushed before the game is saved and closed. The other idols name card is slightly darker and cannot be selected)