If we fall asleep during a session for an interval or this happens to one of our students, does all healing stop during that interval for anything not in conscious awareness but stated in the recording of the Protocol prompts?

This is one instance where we can use the overall intention to support the whole and its parts as well. So a momentary lapse when there is inattention or a drifting into Delta sleep will not be an impediment to achieving full efficacy. Keep in mind the subconscious is still aware even if this does not go up to the conscious level. So there is an additional backstop present, in any event, from that capability. But the overall intention is in most cases sufficient. If there were a wholesale abrogation of duty for the majority of a session that might be different, but what you describe is still within a reasonable range of potential to still achieve the desired end result.