Sorry to revive an old thread but this is exactly the problem I'm having. I have a 2012 iPod Classic 7th gen 160GB which has worked absolutely fine* until recently when it started skipping songs. *(it was an Apple replacement for my 120GB 6th gen which had battery issues but otherwise worked perfectly)
The first thing I did was to do the Apple low-level HDD diagnostic which passed fine (no disc errors, nothing), reformatted and restored the iPod in iTunes but same problem. I then restored and reduced high-bitrate songs to 128kbps - same problem. I then deleted a couple of albums which I knew definitely skipped then re-synced so they were gone from my iPod. I then re-uploaded them to iTunes at a lower bitrate then re-synced. Unfortunately the same tracks in the same places still skipped (yet some played practically to the end).
In the interests of Science I bought a good iPod Classic 30GB 5.5 gen (it wasn't very expensive) and did the same tests as above with the same result.
I listened to the same songs on my iPhone 6 (also from my iTunes library) and they played fine - as did the songs in iTunes.
So what's going on here? Identical problem with skipping songs on two different iPods - one of which I've had for may years with no issues at all. It could be a complete coincidence that two different iPod Classics of different generations could exhibit the same fault but I doubt it. Could it be something to do with the latest version of iTunes (I'm up to 12.0.71 64 bit) not being compatible with obsolescent iPods? I love the simplicity, battery life and capacity of the iPod Classic, the fact I can put my whole collection on there (and even vinyl rips) and that I can keep my music separate from my iPhone to avoid draining its battery (who wants to be stranded without a battery unable to book a taxi or look up train times? OK first world problems but you know what I mean.).
Any help I'd much appreciate it!