iPod shuffle keeps disconnecting

Okay, I have an older iPod shuffle that we got used. The cord that came with it worked fine, but we've since misplaced it and got a new one on eBay when we couldn't find the old one which we just got in the mail today. However, when I plug it into iTunes, it connects briefly, and then it disconnects. It's done this several times, and when I tried to add new songs to it, it actually disconnected in the middle of the transfer and gave me the dialog box that comes up when a storage device is disconnected improperly. When I plugged it back in, it told me the device was corrupted and needed to be restored. I managed to get the device through the restoration process, but it's still not staying connected long enough for me to re-add the songs that were on there before, let alone add any new ones. I can't access it from iTunes, nor from my Finder window. Sometimes I can see it in Disk Utility, but only see it, not do anything with it.

Is it because of the cord, or is it because the battery was depleted and I need to just plug it into the wall and let it charge for a while before trying to sync it?

BTW, I'm connecting it to a MacBook Pro running Mac OS 10.6.8.