IPhone 4S keeps turning off?

My iPhone runs out of battery and when I put it on charge it starts up as normal (displays apple logo) but a few seconds after the password screen is up and the phone is ready to use the phone will shutdown (I usually have just enough time to enter the password before it shuts down).

I have noticed that instead of the battery showing the charging icon, it shows the red low battery icon instead.

I really do not want to go to the apple store to get it checked out. Any help?

Thanks:)

Although you don't want to go to an apple store, you should before it leads to it not turning on at all! Make sure you keep it charged enough and it might need a new battery. :)

Believe it or not, but batteries that you charge will go bad. It is surprising to here it from such a new phone, but your more susceptible to it if you let you phone die and then charge it. It also could be a bad charger. That one is easier to figure out. Just borrow a charger from a friend. If that works, you know you have to get a new charger. If not, you know it is the battery, or at least lets hope it is. If that doesn't work, the apple store trip might be worth your while cause that is a problem we average internet techie people can't solve. Good Luck.