I don't have a 160 GB Classic, but a 80 GB Classic, and it is 2 years old (I acquired it in January 2008).
It used to sync fine for two years, until I moved to iTunes 9.0.2.
I have charged it completely with my USB cable for a whole night (until it said "charge complete"), but the problem persisted, it was still automatically ejecting the iPod as soon as iTunes started (without iTunes running, it stayed connected, and I could even access the hard drive in disk mode without any problem).
As I was getting tired of not having any music, I downgraded iTunes to version 8.2, reloaded my music and rebuild all my playlists (as this was the only way to recover them, since I had moved the music on a media server, so the playlists of the old libraries didn't work any more).
With iTunes 8.2, it now syncs fine.
But I'm still interested in getting a resolution for iTunes 9.0.2, because my iTunes 8.2 often takes up 100% of the CPU, which forces me to kill the process, and I didn't have this problem in 9.0.2.
So any further input to resolve the issue is more than welcome...
JF.