Chances are the iTouch OS isn't located and therefore it can't turn on.
To fix this you can restore it using iTunes.
If you have data on it and want to back up connect to your computer and take a pick out of any program from the link (in the related links below) that does what you need (preferably for free).
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It doesn't actually randomly shut off. It auto-locks to save energy. But you can go to settings and change it to auto-lock less frequently or you can set it to never auto-lock.