The good news is Apple's support was again fantastic. The cable was covered under warranty. I had a copy of my receipt and I had registered the iPod with Apple Support. After a quick chat with a specialist, she set up an appointment for me at the Genius Bar just a couples of hours after our chat. I took the cable back along with my receipt to show the serial number of the iPod and I walked out with a new one. I'm wondering though is there a design problem with this cable. And, like all Apple accessories, it's not cheap listing at $19.00. My first thought was that we were going to have to buy a new one. I did find out, before I checked on the warranty that MonoPrice makes one for less than 12.00. As of the time I'm writing this, they are sold out with an ETA of almost 2 months for the 3 ft white version and there is a limit of (5) per customer. That is another indication to me that there might be something wrong with this cable. Why such a huge demand for something that ships with every new iPhone 5 and iPod Touch? People might want additional ones, but I suspect a lot of them are failing. Amazon also has one for $15.
AmazonBasics USB A to Lightning Compatible Cable (3 Feet/0.9 Meter)