This a similar problem I have like Dannies "I had the same problem with my iphone 5 after updating to 7.0.4. For one month the phone was doing well than the symptoms started. First the phone had 60% off battery i plug it in the wall charger and after 5 minutes it turns off. I did a hard reset and the phone boot properly. Than i plug it another time and after 10 minutes i went to check and it was down again. My wall charger and usb cable are genuine. I tried with different charger and usb cable but with no results.
That i tried to charge via PC and i had sucsses. Than another day the phone had 93% of battery and using 3G on youtube the phone crashed (turn off). Then again and againg using the 3G. I kept charging the phone via PC those days because with the wall charger it shuts off, in the same time i didn't use 3G and cellular data, only wireless. The phone went fine for 2 days than it started crashing again and i had to do a hard reset every time to get it back on because the screen went black. Also on the diagnosis section it started creating panic.plist and reset counter. I searched on web for fixes and did a restore to 7.1.1 puting the phone on DFU mode. The phone got worse after the update, it started crashing every 5 minutes, with 3G, celluar data, wireless ON or OFF it didn't matter anymore. It started a new symptom with the battery full or half or any time i pushed the sleep/wake button after 1 minute the phone turned off, every single time and i had to do hard reset."
Its so frustrating and annoying because I just upgrade my Iphone5 to the lastest version 8.1.2 or so I would have checked it but right now its not comming on. I have to wait for 1 hour. Sometimes if am charging it keeps going on and off without booting completely. I love iphone but this is really annoying. Am in Nigeria there is no Technical support how can you help me with my iphone 5. Please help me.