Hi there Linda,
Welcome to Apple Support Communities.
It sounds like your iPod nano is resetting unexpectedly and you're not able to use it or restore it with iTunes on your Mac. If you haven't already, try putting your iPod nano into Disk Mode as shown here:
Putting iPod into Disk Mode - Apple Support
- Before placing the iPod into Disk Mode, verify that it has a charge.
- Reset the device by pressing the Sleep and Home buttons simultaneously until the display shows the Apple logo. This should take about eight seconds.
- When the Apple logo appears, press and hold the Volume Down and Volume Up buttons simultaneously until the device enters Disk Mode.
Then try to restore the iPod as shown here:
Use iTunes to restore your iPhone, iPad, or iPod to factory settings - Apple Support
Ciao.