It may be an issue with the USB port on the iPod side. Earlier versions of USB (pre-C) ports had a finite number of connections they should support, which aren't larger numbers.
See here:
https://en.wikipedia.org/wiki/USB_hardware
It's up to you whether the repair cost is worth it. If you're curious, contact several third-party electronics repair shops, and don't be shocked by the price, which I expect to be around $200.
You could also do it yourself - see a few resources below, but then you need experience with micro soldering and specialized repair equipment.
NOTICE: The repair of this iPod Touch 6th Gen Dock Port Flex Cable Replacement in Black requires special equipment and knowledge. Please be advised that only experienced technicians with micro-soldering machinery should install this part. The iPod Touch 6th Gen Dock Port Flex Cable Replacement...
www.repairsuniverse.com
These guys say they will do it for only $99:
Description This service is to repair/replace your broken Apple Ipod Touch 6TH dock connector. You will need to mail the Apple Ipod Touch 6TH in for this repair service. The processing and repair time frame for your Apple Ipod Touch 6TH once received is typically 72 hours. You'll be notified...
outsourcerepairs.com
But then again, you could buy a brand new 32 GB smartphone for only $95:
Buy SAMSUNG Galaxy A12 A125U 32GB GSM / CDMA Unlocked Android Smartphone (US Version), Black at Walmart.com
www.walmart.com