The only time the playlist shows up is when I openmy ipod . When I go back to the store it has only the default playlist names listed on the left.
Ok, click on the button to open your iPod's syncing screen.
Click on the section that says "On my iPod"
Click on the playlist you want to sync to the new iPod
Right click on the name of the playlist and select export
Save the playlist file inside the Playlist subfolder of iTunes
At this point, the playlist should show up in your iTunes library
Plug in the new iPod and you should be able to sync the playlist to it now