When you’re doing walking meditation, you mention that mindfulness is not continuous whenever you turn around. But if you’re mindful, you can be mindful of anything; then why should mindfulness not be continuous?
Mindfulness is not continuous if you’re paying attention to the objects. You walk and you’ve targeted something to observe – your feet, your movement or whatever – and when you turn, it’s not the same object anymore. So, you feel like you lose mindfulness.
If you are aware of the mind and what it is aware of, then you walk and when you turn, you continue to be aware of whatever the mind picks up when you’re turning. Then, mindfulness should still be continuous.