Can a battery which has been short-circuited, to work again?

My battery had been short-circuited and my iPod Touch wouldn't turn on, but after 10 days, I charged it again, and it turned on! Then I unplagged it from the ac adapter, and started using it. When I realized that the battery was running out of charging, I pluged it again on the ac adapter, but nothing happened, it wouldn't be charged. So I replaced the old battery with a new one which worked only for 3 days and then it broke down without any reason. But after 2 days, I desoldered and then soldered the second battery (again) and my iPod turned on, but after 10 minutes it stopped working completely. Could anyone help me, please?