By now I am sure we have all heard about the guy who got a new trial in his death penalty case on account of Twitter.
http://www.swtimes.com/state_news/article_090f6530-2275-11e1-aeef-0019bb2963f4.html

But another point raised in that appeal was the fact that one of the jurors fell asleep during the trial.
(Dimas-Martinez's appeal lawyer also argued last month that a juror who was caught apparently sleeping in the jury box while evidence was being presented should have been removed. An attorney for the state argued that the juror had heard "the vast majority of the evidence."

The Supreme Court said Thursday the juror should have been removed.

"Contrary to the state's position at oral argument of this matter, it is not acceptable for a juror to doze off as long as the juror hears the 'vast majority' of the evidence," Corbin wrote in the court's opinion.)

How should someone handle a situation in which a jury member falls asleep during your portion of the trial? If you stop and say "Hey, wake up!" or something similar, you risk pissing off the jury member. But if you do nothing, you risk a retrial.

And what do you do if you notice someone fall asleep but the otherside doesn't notice it?

I'd probably ask to approach the bench and have a short break. The jury won't know it's not for evidentiary/legal issues, and it'll wake them up.

Since this has happened to me let me chime in.

I simply turned to the Judge and casually inquired if we might take a short break since one of the Jurors had fallen asleep during my riveting testimony.....the Judge quickly agreed and handled the issue appropriately....

Remember a case where Defendant was on the stand and a juror fell asleep. Defendant noticed and worked the juror's name into his answer and the juror woke up and stayed awake!