I believe I had the same problem with Final Fantasy Tactics. I dug around and found a PS One memory card and everything was just fine. I assume, of course, that you are playing on a PS2...
What everybody else said. You can only save PS1 games on a PS1 memory card. You can transfer those saves to a PS2 card, but only as a backup. To use them you'll have to transfer them back to a ps1 card.