Hi,
I'm having the same problem with my Nokia Lumia 520, where it just randomly turns itself off. However, I did drop it, but it did this before I dropped it. I have had the screen replaced (by carphone warehouse) and the problem has got worse. Now if it turns itself off, and I turn it on and it's reset itself, it doesn't update my messages or alarms! I have to delete the conversation in order to get a new message and for it to show a sent message. Also, I have to turn my alarm off and back on again! I tried using the folded paper trick, but didn't really understand where to place it, as it worked for a bit, but then ultimately the problem returned. So is this 'normal' with the phone turning itself off and resetting itself? But it's definitely batter related, as mentioned previously, in connection with the initial restart/shut down.
Any help greatly appreciated! And already checked Nokia, I can't claim it off the warranty :\.