This Bt remote http://www.amazon.com/gp/product/B00SCOAL0K has a Micro USB socket for charging. When connected to ext power, it does NOT go to sleep. And when not being touched for (say) 40 minutes, key events are still being sent immediately. - This device still has a flaw: when disconnected from the host device (which will happen eventually, when you suspend the tablet), it will not always reconnect automatically - or at least not quickly. Then you have to fiddle with it's power button, etc. Another flaw: the buttons are really very small on this device. - But overall, this device shows, that it can be done.

Maybe of interest: https://news.ycombinator.com/item?id=11141125