Apple TV remote will not charge

Please note that the remote is not made to indicate that it is charging. It will only be visible through the increasing battery level in Settings on Apple TV.

And charge either through a computer USB port, or through a USB power adapter in an AC socket. Other changing methods may not work.

Charge the Apple TV remote - Apple Support

could be

dirt or lint in the ios devices port when that happen to me I clear it out with a match or toothpick

a defect cable, testing with another cable could show if it is so

a defect port in the device