As far as power button are you turning it off off or putting it to sleep? I ask because if your Ipad is downloading, say a video, when you put it to sleep it will continue to work on the download and videos suck a lot of juice playing and loading.
If you have a bunch of stuff running in the background it will cause less than desired results. You can double tap the home button, hold any app that shows up along the bottom until a minus sign shows up and tap the sign on all you want to close or you can buy an app called xsysinfo that basically does it for you .
If you can hotspot your Ipad via a mifi type device and turn off 3g your battery life will be considerably better as well.
As far as the sudden black, it sounds like your Ipad for whatever reason went to sleep. If that happens again try pressing the home button and see if it actually is asleep. If so go into your settings and change the sleep time to never.
Hope that helps
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