I skipped over the middle of this thread when it seemed to degenerate into a juvenile pissing contest, so someone may have already said this. I don't know one professional pilot who would intentionally jeopardize his job and the safety of his passengers. So, if your cockpit co-worker happens to fall asleep, realize that it wasn't an intentional act and also realize that if he/she could have stayed awake that they would have. Most likely, the next radio call will rouse them, if not let the poor guy sleep until you need him/her. I figure that a rested pilot does me more good than one who expends all his mental energy in an attempt to stay awake.
That's advice for dealing with someone who just can't stay awake. If you've got someone who habitually drops off, it is your duty to him/her to have a talk with that person.
As for me, If I get so sleepy that I can't keep my eyes open, I will let my FO know that I'm having a hard time staying awake. I ask them to keep their eyes on me and wake me up if they notice that I've conked out. That way, if I nod off for a second they leave me alone, but if I begin to snore (i.e., obviously asleep) they wake me up. I wouldn't want my FO to be sitting there wondering if he/she should wake me up. Nor would I want to try and explain my lack of consiousness to the accident investigators.
I equate the the inability to stay awake to an illness that incapacitates you, but unlike coming down with stomach cramps the inability to stay awake will go away after a very short cat nap. Let him/her snooze, wake them if you need them and then ask them if they are OK after they wake up. There may be more wrong than just sleepyness.
Bottom line. Take care of your partner. He/she would do the same for you.
enigma