iPhone 5 dies at high percentage, comes back to life at same percent

My iPhone 5 dies at a high percentage, for example 80%. When I plug it in and it comes back to life, it's going to still be at that same percentage or maybe just a little lower. The phone works perfectly fine besides just that. It's a June 3, 2013 model and I have it running iOS 6.1.4. What should I do?