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That usually means that there is some issue with the battery itself. This could possible stem from the charging cable. However, if the unit is charging properly, and functions normally otherwise, you don't really need to worry about the LED. The mechanism that Panasonic uses to determine the battery health isn't that great on that camera, and often has false alarms, and there is no real way to correct it.
One thing you can try is replacing the battery with a new like in the link below:
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