Typically I would take that to mean it was time to get a new one but not this time. I noticed that the charger was slightly bent (not surprising after all the moving I've done!) I have the 1st Generation shuffle, which they no longer make. Chargers run roughly $30 at the Apple store, which is still more than I wanted to spend. Then I hopped on Amazon and found a similar 2nd Generation charger for $3.94 including shipping. That's what I'm talkin' about! Now it works and everyone is happy!
Just in case the different generation charger didn't work, I also found an arm band for my larger iPod so I could run with that if I needed to. It was only $4.95 with shipping. Not bad at all!
Now I can skip the gym on the weekends and run around the reservoir instead. Good timing, too, because I'm going to run my first 5K in October and I have some serious training to do!