Sorry but you have not confirmed that your USB cable works properly with your Kindle. I have several cables that work with my Clara HD but not with my Kobo Glo HD or PaperWhite 10th gen and vice versa.
IMNSHO, your comment about the connection going now you see me, now you don't suggests that either the cable or the USB connector on your Kindle are flaky or the Kindle is attempting to draw too much power from the port. You could try a powered USB hub in between.
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