Just encountered this mindblowingly annyoing issue with iTunes 12.7 and Sierra 10.12.6. Never had anything like this before! I will submit this thread to Apple, this is focking ridiculous how low their QA standards have fallen over recent years. Some debugging points:
1. Issue is only with mp3-files. In my case skips at 39-40 second mark. Such skipping counts as PLAY, not as skip though!
2. Deleting problem tracks from the library and re-adding them fixes (now **** wish me luck with readdding 1000s of files across dozens of playlist... Do they even know how laggy iTunes gets when readding stuff from afp:// network drives???)
3. Happens to files that been added to library ages ago! And does NOT happen to files that been played before today. E.g. I have an album, that I haven't finished listening too, so unplayed tracks are problematic, but those that I played before are fine.
4. I don't use any services like iTunes Match, Apple Music or other crap they offer, signed off their slow glitchy appstore just to avoid the whole ordeal altogether.
5. Makes me think it's something to do with number of tracks in the library, as today I added couple more albums and my library is getting close to 32768 files (32598 to be exact), so maybe some ancient 2^15 limitation or whatever they were thinking / snorting back in 1998 when iTunes was conceived.
p.s. iTunes NEVER been brilliant tbh, but at least you COULD put up with all that buffoonery and adapt to it, so you COULD listen to your music. Not anymore I guess. Closed ecosystem my *** (I mean, you still need iTunes to sync your devices, otherwise some decent music player would de-throne it overnight).
/rant