My iPhone automatically shutdown when not using

Hi, I just bought an iPhone 4S for 2 weeks and I notice that it turned off 2 times even it had about 40% battery. I had to hold the Lock button to turn it on. But today it automatically turn into sleep mode something like that at 35%. I had to hold both Lock and Home button to turn it on. When it was on, there were only 5% battery left.

I'm very confuse and do not know why my iphone acting like that. Can anyone explain this to me? Is it an software error or hardware such as battery error? I did research some web pages and still haven't found the exact problem.

Many thanks