Rick is a teacher and he did a science experiment with a weather balloon and his GoPro. But it shut off after a few minutes, even though he had an external power source. What happened? Leo says that Lithium-Ion batteries don't do well in extreme temperatures, and several thousand feet up, it's -40 degrees up there. So it's likely the camera batteries died because of the cold temperatures. That's why those who do this, use an insulated box to house the camera and batteries.
Some use hand warmers to keep your batteries warm during the flight. Also, use a juice pack that uses standard lithium AA batteries. Check out this Kit - http://www.alioth.io/high-altitude-balloons.
Here are a few other links to look at: