Highscore doesn't safe

I just got myself my first Gameboy with some Games (Tetris, Solar Striker, MIB the series). The problem is, that when I close the Gameboy and start it again later, the Highscore disapears. For example: I played Tetris And got a certain ammount of Points, and as Long as I don't close the Gameboy, the Highscore stays, but when I close the Gameboy and start playing again the Game says there is no Highscore at all!