A psychologist I know (not my T) once conceptualized the T who falls asleep in session as someone experiencing a similar phenomenon to what psychoanalyst Harry Stack Sullivan, who is known for the development of a school of "interpersonal psychotherapy", described for infants. Sullivan proposed the concept of "somnolent detachment", which would be a baby falling asleep in response to an anxiety-provoking situation or caregiver, in order to escape awareness of the situation and the stress. The guy I talked to (a T himself) said that therapists sometimes fall asleep in session the same way. I don't know... such a T would probably have a long way to grow up

But seriously... I met people with sleep disorders who do what the OP describes. They actually do fall asleep for short periods of time even during a conversation but learn to mask it reasonably well (or not) and would not admit because it's so bizarre. Many people develop sleep issues as they get older, for example sleep apnea, that can really interfere with daytime wakefulness and is not easy to control with willpower.