The issue with not saving campaign progress got addressed in several patches but some players have still issues with the campaign progress.
I recommend to delete your BF4 game from your Xbox One hard drive. After that, log out of your profile and reset your Xbox by pressing the Xbox button on your console for at least 10 seconds. After your console is back online, sign in and install as well as update Battlefield 4. Try to play several campaign matches without jumping in a multiplayer match and check if your progress is saving now.
Cheers
Basti
