How long have you had the phone? It shouldn't be rebooting on its own like that. Is the phone overheating? Any recently installed apps that could be using up a lot of juice? Have you tried a battery pull? I have a G3 and battery pulls have saved me a couple of times!
My advice would be to take it back to ATT if you can. Or contact LG customer support online.
After two visits to AT&T store and no fix, I called LG technical support and they will send me a new replacement. Will see how it goes with the new phone.