If you've had your card open for at least a year and decide the benefits aren't worth it for you, you won't lose your miles if you decide to cancel. Your miles are kept in your Delta frequent flyer account, not your Amex account. However, canceling a card before you've had it for a year may result in having your welcome bonus offer clawed back, so it's not a good idea to close a card until your first 12 months is up.