Mine will play for a while, but then just quit playing.
Is it running out of battery power?
What happens if you turn it OFF (with the switch), wait about ten seconds, and turn it back ON?
I will try and plug in the ipod headphones right away but they won't work either then.
Can you describe that again in more detail? Not sure what you mean...
Let it sit for a few hours and then it is fine.
Do you turn it OFF (with the switch) during that time, or does it stay ON?
If you have not already, you may want to do a Restore on the shuffle using iTunes. For a 3rd gen shuffle, select the shuffle in the iTunes sidebar, under DEVICES. Over to the right, go to the Summary tab. Click the Restore button. This will erase the iPod, re-install its software, and set it to default settings. NOTE: If this is a 2nd gen shuffle, it's the Settings tab, not Summary.
Then, reload some songs and see if the problem recurs.