My iPod 4th gen and it has gone dead, it works when connected to iTunes but after disconnecting again goes dead.PLEASE HELP.

My iPod touch 4 is not working at all,I tried every possible way like pressing home and lock buttons together but not results. Also, when I connect it through USB to my iTunes It switches on and works well but when I disconnect it works for 5-6 min and again goes dead! I tried restoring it completely, it worked well for at least 2-3 day and then again became dead! Is this battery fail problem or something else.PLEASE HELP. I hope it will be cheap to repair it.