Oh boy -- this sounds like the problem I had many months ago. I hope I can give you some insight, as it was very frustrating to deal with (although I eventually resolved the problems with the tracks).
I had found a very useful thread on the Apple support forums. However I had to pay attention to the info from posters who had "the same problem" and filter out those that had similar-sounding-but-different problems. Of course you'll have to apply that filter to me too...
Going by memory, "the one true problem" seemed to have these characteristics:
(1) It could occur in many versions of iTunes. Some sufferers were on the latest version, while I was (and still am) on iTunes 10.7.
(2) A given song would always prematurely end (skip to the next song) at the same point in iTunes.
(3) A group of songs all imported "at the same time" all had a similarity about the point at which the skip occurred -- I think they all skipped at the same number of minutes/seconds into the song. Songs that were shorter than that length did NOT skip and were fine.
(4) Playing the .aac or .mp3 file itself with another player worked fine (no premature end) -- even if you used finder to get the file out of the iTunes Library. (Thus, the aac or mp3 file itself was NOT the problem.)
(5) You could fix a given song as follows: within iTunes, right-click a song and pick "Show in Finder". Then re-import THAT SAME FILE into iTunes. I think I just dragged the shown file from finder and dropped onto the iTunes Library pane.
(6) For me at least, the problem never occurred when I ripped a CD into the library. It only happened when I imported an album's worth or more of mp3 files by dropping them in iTunes. Then, I would consistently get *some* tracks with the problem, but the exact minutes/seconds at which the early termination occurred would be different than the last time I tried importing the same files (thus more or fewer of the tracks might exhibit the skip due to the length of the tracks and the new timing of the skip).
(7) An early termination was more likely to occur in the longer songs. I could often find if an import had a problem by picking the longest song, setting the playhead near the end of the song and hitting play. If it immediately skips to the next song, you've found one.
(8) Oh, some sufferers were using iTunes Match and at first thought it was the culprit, but that turned out not to be the case (at least for "the one true problem").
From these symptoms, I think that the problem is not anything in the .aac or .mp3 file itself. Rather, I think some values are set incorrectly in the iTunes Library
File itself (sorry don't remember the filename -- .itl? there is also an XML version of it but that's not the exact file I mean). Some info about a song is kept in the song file with ID3 tags, but some other info about a song is kept in the iTunes library file. This is why re-importing the exact same song file can fix the problem -- because the info in the library file is re-written.
As I said, I never had a problem importing from CD or importing one file at a time. I think there is a very subtle bug in iTunes where the importing goes awry when certain timing or load conditions are met when importing multiple files.
My only solution was to either import from CD, import one file at a time, or check for "problem" songs and fix them as in (5).
I hope you don't have the same problem because it was a real pain in the neck, but if you do I hope this helps. Good luck!