My phone shutsdown and shows low battery even when charged
For the last month or so, my iPhone has been shutting-down by itself as if it was low in battery charge. When I try to turn it back on, the phone shows the red battery-low symbol and refuses to come back on. When I plug it in to recharge, it comes back on, and starts working fine again. This has been happening with the phone having between over 30% charge.
I have an iPhone 4S, with all the software updates done.
iPhone 4S, iOS 7.0.4