instal the new version for ipod ClassicDesktopClock 4.44

I've rebooted them both (the third iPod I've not involved in any of these tests), but that makes no difference. I don't know what to make of this except to think that the problem seems to reside in the iPods. I suppose it's possible I was using an even earlier version, but I have deleted earlier versions of my library backups, so will doubtless run up against that problem if I install earlier iTunes. I'm reasonably sure that I would have been using one of these 5 versions in January when I was last able to sync, but now none of them works, (whichever one it was). (This was the ipod whose driver s/w I hadn't updated through Control Panel. For a moment, it looked as though it was going to work, but after being connected for several minutes, iTunes popped up a message which said that my iPod seemed to be corrupted.I disconnected it and connected the second iPod, which didn't get this 'corrupted' message but went through the rapid connected-ejecting cycles. Now iTunes wouldn't recognise the December library, and so I had to use an earlier one, backed up in August. So, I went through a further 4 uninstall and reinstalls of previous releases (interestingly, I was able to use the same library, even though that was created after the date of each of these releases) but none of these resulted in a sync, so I jumped a couple of upgrades and went to 12.4.1.6, which was released in June '16. I then thought I'd try earlier versions of iTunes, but the problem was that as I don't upgrade iTunes every time there is an update (which is just about monthly), I had no idea what version of iTunes I'd been using before upgrading to 12.6.0.100, and which I was therefore using in January when I was last able to sync. So I tried the 2nd iPod, with the same result. However, the iPod was still not recognised by iTunes and I got the same behaviour (several connected-ejecting cycles per minute) while the iPod was connected, and no recognition of the iPod by iTunes. That wouldn't work with my (current) iTunes library, but fortunately, I back up the library and so replaced the current with the previous one created in December. The last time I was able to synchronise was in January (not April as I said before) so I uninstalled the current iTunes and installed 12.5.5.5.

So I then looked at the second option - to roll back to a previous iTunes. I only followed this with one of the 3 iPods. I looked at the first option you suggested (driver update), but that didn't change things.

Instal the new version for ipod ClassicDesktopClock 4.44