There may be a hardware problem on the iPod nano, which is why it continues to appear in "recovery mode."
Try this... while the iPod is connected to the computer and iTunes is running, do this Reset procedure on the iPod.
If that does not help, if the iPod is connected using a USB hub, try connecting it to a direct USB port on computer. If you have a lot of other devices connected to the computer's USB ports, try shutting down (powering OFF) and disconnecting all USB devices. Start up with only standard keyboard and mouse connected (if used). Then run iTunes and connect the iPod to a direct USB port on computer.