I've got the same issue, but in my case, they're AAC files encoded with NeroAAC rather than from iTunes.
Sometimes it will play the entirety of 3 to 4 tracks, and sometimes it will skip to the next track after 2 to 3 seconds, several tracks in a row. As indicated by the OP, sometimes the player turns itself off after altogether.
Information which might be relevant or helpful:
Sansa Fuze V1 8GB with Rockbox 3.8.
When the skipping occurs, there is no pop or hiss or any unusual noise. It simply advances to the next track silently, and begins playing. Initially I thought it was perhaps a button issue, but it does this even when the buttons are locked. I also tried turning on "Disable Track Skip", but it had no change. Finally, I enabled the option to beep when skipping tracks, to determine if the player was advancing due to some erroneous input. It does not beep when this fault occurs, so it does not seem to be a button input error.
This issue does not seem to occur with FLAC files, which are the only other ones I've tried since the upgrade.
I did not experience this issue (or at least, it was infrequent enough that I never witnessed it) with 3.7.1 (or perhaps 3.7 -- I've forgotten which I had before the upgrade. I suspect 3.7.1.) The audio files haven't changed.
This does not always happen in the same spot or with the same files. It's random as far as I can tell.
Possible it's related to this similar issue with WMA Pro files?
http://forums.rockbox.org/index.php/topic,27518.msg179225.html