I'm assuming that you're playing on the original PS? Your memory card may just be full. I'd check to see how much space your memory card has on it/how much space is required to save the Back to Nature data before deciding to use a separate memory card.
If you're playing it on the PS3, you'll most likely have to 'create' another memory card for the game to save on. When I started playing mine on the PS3, I found that each memory card didn't have much space and so I had to make a separate one. I keep that one for Back to Nature data.