I have a similar problem but this solution is not working 😟. Have tried the 'CPR' treatment many times recommended by planb77 but just get the Apple logo followed by shutdown.
My iPod Classic 6th generation about 2 years old froze on the music menu, battery ran down and when I connected to iTunes to recharge and sync the message on the IPod was 'do not disconnect' then 'Ok to disconnect'. It wasn't able to sync with iTunes.
Took it in to the Apple Store, it did the same on their notebook, and diagnosed it as a firmware problem. They offered me a reconditioned iPod or a new one with a 10% discount for mine.
I expect greater longevity for 'quality' products that have been well looked after. Maybe I was unlucky and just bought a dud. The iPod also needed repair during the warranty period.
Any solutions out there?