Here's an answer to a similar issue on an iPod Touch, it mostly applies to your device as well:
I'd try to determine where the fault lies first:
1- Try a different iPod or iPhone to check if issue is with cable or iPod.
2- If issue is with the lead, try using a better/genuine product;
3- If issue is with the iPod,
3-A/ If the songs you are trying to play are stored on your iPod: try cleaning the dock connector (where the charging cable plugs in) using a soft toothbrush dipped in 90%+ isopropyl (rubbing) alcohol.
3-B/ If the songs you are trying to play are streamed to your iPod: check that your Wi-Fi connection is fast enough. Or play the songs on your iPod and see if they are running well or they also intermittently stop playing.
Go through the above to start with, and let us know what you find out or if your issue is fixed.