Have a 1st gen 32gb Nexus 7, it was exhibiting this behavior, it started out f the blue 2 days ago, and was getting really annoying. I tried the case fix, nope. Tried the auto brightness fix, nope. I was reading about it in the dark with the auto brightness off and it did it twice and I noticed, the screen would dim a precise amount and then go black. This was just how the sleep function behaved. I went and looked, no sleep interval was set, set it for 1 minute, it had been an hour, all is well.
Tldr: try setting a sleep time interval.