Help -- iPod Nano loses charge quickly and won't start up

I read the link re: hibernation, which applies to the Nano. Deep sleep apparently does not. Essentially, I turn the Nano completely off by pressing the play/pause button. After, say three days, when I try to turn it back on, no matter how many different buttons I press, including Select, it will not turn back on. It will only do so after I hook it up to my Mac.
Another odd thing. I charged the iPod all night on my Mac and it was fully charged. When I put the hold button on for awhile, and then took it off Hold, the battery was more than half used, and I hadn't even used the Nano. I'm totally puzzled.

I'm going to test some of the things you're suggesting and then send you a reply. I hope that's OK and you'll see my message and answer me.
thanks for all your helpful suggestions.

I spoke with someone at the Genius Bar yesterday at the Apple Store, and he told me that if I don't use my iPod for a few days, even though it's turned off, it will completely lose the charge and that's why I'm experiencing this problem. He said that technically, the Nano is always on, even though it's "turned off." So, do I always have to have the iPod connected to a charger when I'm not using it, even though it was charged when I stopped charging it?