I've had my iPhone 6 for about 14 hours and it just turned off by itself at 60%. It did not even run a full battery cycle. Now when I restart it the Apple Logo comes on then goes away. Put it in DFU Mode but wont let me restore. When I take my finger off the home button in DFU mode the phone shuts off. Disappointing that my first iPhone 5 64GB came without a front facing camera and now my iPhone 6 128GB just takes a **** on me before its even 24 hours old. Any suggestions besides the obvious visit to the apple store?
The only thing I might suggest is to try to plug it in and let it charge it for a bit... perhaps the battery is flat even though it was showing 60%. My guess is that won't help, but it might be worth a try before you take a drive.