There are three different versions of the GameCube Action Replay. If your Action Replay card has a purple AR sticker then you have the standard version of the GameCube Action Replay and the AR card will not be able to save game progress and the GameCube will not recognize it. But if your Action Replay card has a white AR sticker then you have the limited edition version of the GameCube Action Replay and the AR card will be able to save game progress.
The very latest version of Action Replay GameCube doesn`t come supplied with a memory card.