Why does my iPhone dies on its own, but when i plug it in, it's half charged?

So my iphone keeps "dieing" out on me, but it is half way charged when i plug it in, it is so annoying, what can i do?
someone please help x_x
i don't have any apps running in the background i'm always closing them, my phone is about 1 month old, bought it from someone, and they hardly used it (i could see by no scratches on the phone)
i use a blackberry wall plug in with the normal apple chargers.
i don't know what else to do

It actually sounds like the person that sold it to you might have damaged it. It could have been in water or dropped, so no scratches but damage done, I wouldn't go by scratches as a factor in determining something like that. Do you really think someone had an iphone for a long time and "hardly used it"? Sounds fishy.
If you have an apple store near you, you might have to have them examine it.