iphone 3gs turning off after updating to 6.0.1

Hello, i have a iphone 3gs that i recently updated to iOS 6.0.1. After i fully charge him, i try to see the emails or play a game and he simply turns off. Then only way to turn him back on is by puting him charging. ( yes he had full baterry) i have tryied to dowgrade to iOS5 and the samething happens.

any help plz?