Hello Singhindia,
It sounds like you restored your iPod Nano when iTunes prompted you and it appears to sync. When you disconnect it and look at the content, the songs arent there, and when you plug it back into iTunes you get the same message again. I would recommend these troubleshooting sections from the following article to help isolate the issue to hardware or software:
iPod nano: Error message saying that iPod 'could not be identified properly'
http://support.apple.com/kb/TS3218
If the issue continues, gathering iPod Diagnostics may be helpful for you or for support personnel in identifying the issue.
Certain phone connectivity software from vendors such as Samsung, Nokia, Bora, Novatel, and Sony may also cause this issue. If you have such software on your computer:
- Uninstall your Samsung, Nokia, Bora, Novatel, or Sony phone connectivity software and test. Contact the manufacturer of this software for assistance in doing this.
- Remove iTunes and all related Apple software by following this article (for Windows XP), or this article (for Windows Vista and Windows 7).
- After reinstalling iTunes, test the iPod nano.
- If you still need your phone connectivity software that was removed, reinstall this software and test your iPod nano to ensure it still functions with iTunes. Contact the vendor of your phone connectivity software if the issue returns.
While the error message is different than you are seeing, the troubleshooting is relevant for you.
Thank you for using Apple Support Communities.
All the best,
Sterling