Iphone 5 Shuts off with Battery Still remaining?

Ok, so this has been happening 2 or 3 times a week ever since I updated the software to IOS 7. Whenever I enter an area with sub-par cell phone service, like the gym or my basement, my iphone will sometimes shut off on its own. Whenever I try to turn it back on there's an icon with a lightning bolt and phone cord, which I assume means that the battery is close to death. However, it will die whenever my phone says it has a battery of 20, 30, or sometimes 40%. When I get home and plug it in, the phone will come to life, displaying the partially full battery that it had before it died, as opposed to showing 0 or 1%. I'm not really doing anything that drains the battery, like surfing the web or streaming video. I usually am just listening to music. My best guess is that my phone is draining battery trying to find service, however, I don't think that would explain why it shuts off so sson, instead of fully draining the battery.

Is there anything I can do to stop this? Has this been happening to anyone else? Any feedback would be appreciated, thanks

Not an answer but I'm actually having the same exact issue. Will shut off around 20-40% battery life left. Getting very annoyed when I'm watching a video or listening to music and it shuts off so soon like that. Would appreciate any help on the matter. Didn't start doing this until the update to iOS 7. I always make sure apps do not run in background and do hard resets weekly or twice weekly. Not sure what else to do.

Exactly the same happening to my iPhone. Obviously a problem with the update.

Mine does the same thing. Makes me seriously consider going Galaxy.
Nothing worse than taking a photo of a milestone event and the phone shutting down.

Mine iphone 5 has been doing the same thing since the IOS 7.1. Anyone find a fix for it?