You're using your phone, aren't you? Not a computer?
Or maybe there's a setting somewhere that I ought to have checked.
I think you have to sign in to your account to save the list - is that right? Mine always saves - I can look at the top of the page and see what I've got in there (number of items and price) but I have an account with the superstore.
My cart never gets saved. I lose it every time I close my browser so I make sure to put everything in the wishlist first instead of the cart. Then I check off everything I want to buy and at the bottom of the wishlist there's an option to add everything that is checked to your cart.