Short Battery Life on insignia 4gb player

I've heard where some batteries have to 'relearn' their charge. Try discharging the battery completely (using the player until it shuts down from low charge). Let it set about half an hour like that. Then plug it in and recharge it, be sure to unplug it just after the charging icon goes green. See if this helps. If you need a new battery, you would probably want to check eBay as they are hard to find other areas online.

Sounds like the rechargeable battery has gone bad.  Replace the battery and don't let the player cook in the wall socket next time.