If you close your American Express credit card and you have rewards in your account, you will forfeit your points balance after enough time has passed. However, you can get around this if you have another American Express credit card that offers the same type of rewards. For example, you could cancel your American Express Gold Card without losing your American Express Membership Rewards points, so long as you also have an open The Amex EveryDay Credit Card* account where those points can live.