Why are we taught not to fall asleep when in a survival situation?

In the film, World Trade Center, the character McLoughlin (Nicolas Cage) and the younger policeman exhort each other not to fall asleep. Why would falling asleep be bad, if such would help the body and mind rest? We are led to believe the same thing in situations involving hypothermia. Let's say we could hunch over, cover ourselves (insulate), and rest or sleep; would this not increase our odds of suvival?
I recall hearing from someone that the latest research shows it is better to stop and rest, if lost in extreme cold conditions, even to let the snow cover and insulate you, rather than waste valuable resources in an effort to stay awake.
By the way, what is the name of the Marine who went in to Ground Zero to seek survivors? What is the name of the actor?

normally in a survival situation you are encouraged to get as much rest as possible as most people don't sleep for days when they are desperate and stressed.

In this movie they were hurt and possibly had much blood loss and shock. If you go to sleep with a severe concussion or you are some how on the edge of death due to bleeding or other trauma, you may go to sleep and not wake up. You have to consciously will your self to live. There is a thought that people will just give up living and not fight to remain conscious.

lost in the woods or in a war you must try to sleep each night even if the fear is too much.

Maybe we wouldn't be able to wake up.

um i am guessing so they won't die