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For a few days now I noticed that my iPhone 5 shuts off even though the battery level is at over 10%, when plugged in it turns on immediately and the battery percentage is the same as it turned off at.
I am on iOS 7.0.3, however this started on iOS 7.0.2.
My wife's I5 is having this issue as well, her's started doing it after 7.0.3 update
Basic troubleshooting from the User's Guide is reset, restart, restore (first from backup then as new). Try each of these in order until the issue is resolved.