My new iPhone 5s keeps turning itself off even if there is battery remaining and when it's on charge
I have recently bought a new iPhone 5s (within the last month) and it keeps turning itself off. It first did it I was charging it overnight (and I was late for work as the alarms didn't go off!) so I stopped charging overnight in case it had some safety thing. But since I did that it still keeps turning off. It says it has battery remaining and has turned off even when I have just taken it off charge. I looked at it yesterday for the time quickly put it down then picked it back up to reply to a message and in that time it turned off!
help!
iPhone 5s, iOS 9.1