Can't sync a song purchased with an old iTunes account that I don't use anymore
I think that technically you are able to solve this problem. 

If you can't use your old iTunes account to download DRM-free version of this song and you don't want to purchase this song again using your current account (this in my opinion, is the fastest and best solution), maybe you would like to export this file e.g. using iTunes Export app (https://itunes.apple.com/us/app/export-for-itunes/id880764359?mt=12&amp;ign-mpt=uo%3D4). 

As says app description from Mac AppStore:


  Export your playlists and albums from iTunes to any local folder, external storage, SD card or USB drive! You can transfer easily your playlists to your car stereo or any other media player. Convert aac/m4a files to mp3 for best compatibility with most sound systems. 


But you have to remember that this app:


  *Can not convert DRM protected files.


So:


In iTunes, you have to add this this problematic song to a new playlist
you have to check this playlist in iTunes Export App
next you have to click Export button
you will see export options





In here you can choose conversion options etc
Next
you have to choose export location
and finally, after a few seconds you have a new copy of your song


Now you can import it to your iTunes library, and try to sync it with your iPod.

But... iTunes Export is a paid app (quite expensive for such a little task), so if you won't be using it regulary to perform similar actions, all above soulution is not worthy your attention;-)

I'm curious if anybody will suggest a better (cheeper) way to do it.