The subject line says it all.
My only guess would be that it’s an evolutionary defense: tired = not able to defend myself = be grouchy to keep potential rivals (and animals) away.
Since you’re tired, your reactions get slower and you get confused and therefore frustrated more easily. This leads to grouchyness. This, at least, is my excuse.
Haj
I’d say defensive as well. As Hajaro already noted, fatigue slows your reactions. It can also impair thinking and perception.
Going through the normal process of ‘I see/hear something. What is it? Is it a threat? What is the best way to react?’ takes too long if you’re tired. Thus, a tired mind defaults to increased hostility in order to display strength and frighten away potential threats.
This is why it happens to some people when waking up as well.
Why the hell did you wake me up to ask me that? Idiot!
I’m not grouchy when I am tired. I have noticed however that whenever I take a nap during the day, I always wake up hot and sweaty and in a foul mood. Does anybody know what causes this?
Perhaps it’s the other way around, we get tired when we’re grouchy. You could define grouchy as being irrationally provoked by small things. Maybe we have another type of defense measure that puts us to sleep before we clobber our neighbors because their nose hairs are too long. 
Could one argue that being grouchy is not in one’s best interest, in terms of self-defense? It seems like picking fights were there would be none normally will lead to self-destruction when one of your victims decides to make you the victim, i.e., fight back. I’d think if you’re tired, maybe being nice to everyone to avoid a guy possibly breaking a beer bottle on your face would be the tactic to use.
Plenty of animals settle things by bluffing-fur stands on end to make them seem larger, then they hiss, spit, growl, roar etc.
Don’t think of how grouchiness affects us today. Think of what happened when Homo Habilis woke up on the wrong side of the savannah.
[indent]:mad: [sup]Go to bed and stop asking silly questions![/sup][/indent]
(Speaking from personal experience)
Well there are other side effects of sleep deprivation that go along with grumpiness such as generally being anti social and avoiding any complicated social interaction. I tend to just avoid socializing, but when I am forced to socialize I become grumpy and defensive. My cognitive functions ussually aren’t working well so I tend to try and get by until I get a chance to sleep.