How about when you're on the run from the cops. Trying to win a game show Swimming away from sharks Doing a live interview In a boxing match During a wedding
I think I will go with this one as well. Though...
while having sex in the kitchen
After sneaking into your girlfriend's place and having sex with her in the living room when her father is way overprotective of "His little princess" and he keeps a gun on hand, ready at all times.
Falling asleep during a test that determines your life. Falling asleep right before getting your first nuke in MW2. Falling asleep during a police interrogation. Falling asleep after calling a cop "Officer Doughnut" Falling asleep in the middle of dinner. Falling asleep while being kidnapped. This list could go on..
Falling asleep in a court room (cop sticks their hand out and sticks out their middle finger and points you to come to them). Never happened but that would suck.
I don't know if this is the worst time to fall asleep but... I have fell asleep before on the floor in my living room when my dog gave me the licking of a lifetime to my face.