I'm confused. The title asks a question, but then in the post, you state that you are given the opportunity to reply to a message when you swipe to the left, and therefore, I'm not sure of what you're asking.
I think OP means they can quick reply from the lock screen by sliding, but they can't quick reply within the home screen, like pulling down the banner message.
Make sure Banners is on within the Notifications section of Messages.