"do not fall asleep while praying" at the end of Chapter 10 Book Three emphasizes, the awareness of praying. It is dedicated to the prayer as a task of consciousness, not to pray automatically, pray in Your own words and not following something You learned by heart.
The other stress is, what Kaeso said.
The exact wordly meaning of the german sentence is: "don't surrender to sleep".
But writing "fall into sleep" directs more to the facts that he explains about the prayer. The prayer is a key to the whole work. I think "don't fall asleep while praying" hits the task of the whole Ritual.