This sounds like a problem with the battery and not connecting to the charging port. Have you had problems when charging? If so, then maybe change the charging cord. If however, after changing the cord and is still giving you problems, then your device can be experiencing problems with the battery.
When did you get this iPhone? If within the last 60 days, then you have the Apple Warranty, and they can replace it for you. If you have AppleCare, then you can take that route.
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