My iPad is crying
I thought it might be my wife's email client which she often leaves in a browser window, but we closed that and the odd behavior continued.
After a couple more days of puzzling, we realized it was happening when the 'Pad was plugged into the wall adapter, and whenever anyone would *come close* to it! It is not necessary to touch it, you just have to walk by it and it will awaken, beep, and then go back to sleep.
Why?
iPad, iOS 4