Q: iTunes track not syncing

First, confirm the song is on the shuffle.  Since the shuffle has no screen, you can do this in iTunes.  Select the shuffle in iTunes (click its device button on horizontal bar) to show its settings screen in iTunes window.  Along the left side (in the sidebar), under On My Device, click Music.  To the right, the shuffle's song list is shown.  Is that song that gets skipped on the shuffle?

So, you have confirmed (using the view of the iPod's song list in iTunes) that the song IS on the iPod...

when I attempt to play it directly, it skips to the next song on the list.

An iPod shuffle does not have a screen to select a specific song.  How are you playing a song "directly" on your shuffle?

There may be general data corruption on the shuffle.  Try doing a Restore on the shuffle using iTunes.  This erases the shuffle, reinstalls its software, and sets it to default settings.  You said previously that you "reset the device," but I don't know if that was a Restore.

Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support

After the Restore, I would initially only load that one song (that has this problem) and see if it still skips.

Weird that it had this problem when you synced the same song as part of a playlist.  That should not make any difference...  But glad you got it to work.