Most GPS units' power lasts -- what?? -- less than two hours. This is fine, perhaps until you need the device. If the power source is drained, through use (unlikely), through defect, through misadventure, you have a problem. Severe ionospheric disruption, I understand, may also cause problems.
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The easiest compass to use in an emergency, I believe, is the Suunto KB-14 360R/D. These are sighting compasses that show the azimuth going and coming, and allow you to adjust for declination.
If you live on the eastern seaboard and take a trip to visit me in Montana, magnetic north is in a different position relative to grid/true north. Most compasses rely on your ability to remember the difference, and to apply the arithmetic to the map. When you're frightened, you might neglect the arithmetic.
Declination adjustment allows you to rotate the compasses degree card at will. When you sight your mark, your reading will match the map. And you can do this in the comfort of your home.
The downside is that convenience costs.