Instructions
Verify that your PS2 memory card is properly connected to the memory card slot on the front of your console. Unlike cartridge-based games like the kind found on the Nintendo 64, PlayStation 2 games are CD-based. Because of this, you need a separate external memory card to save games. If no memory card is inserted into the console, the "Save" functionality of all games will be disabled.
Open the "Memory Card" manager utility in your PlayStation 2's main menu and verify that your memory card is not completely filled. Saving a game to a memory card on a PS2 is like saving a file on your computer's hard drive. If your hard drive doesn't have enough room for the file, the file won't be able to save. If your memory card is reading as "full," delete any save data files that you no longer wish to hold on to, making room for the new save you're trying to create, and then save your game again.
Insert your memory card into the "Controller 1" memory card slot on the front of your PS2. Certain games may not recognize your memory card if you're playing a single player game with the memory card itself inserted into the "Controller 2" card slot. Remove your memory card, place it in the first memory card slot and then try to save your game data again.