Q: Ipad2 shuts down randomly

Hi, my IPad 2 is about 3 years old and has started shutting down randomly. To turn it back on a simple 'power on' using the power button doesn't work - I need to hold both the power and home buttons down together for 10 seconds. After start up it works fine but will eventually shut down at a later time with no cause. (ie there's plenty of battery life remaining).

It's a 64Gb IPad with 46.5 Gb available. I've updated the OS to the latest (V 8.1.3) and even performed a reset and backup while connected to iTunes, yet it's still occurring. Auto lock is set to 10 minutes but I've tried various settings with no improvement.

Can anyone help me?

thanks very much.