I've had this tablet since it was released last fall, and this behavior is very recent.
Anyways, it dies FAST. Like nose dives in a matter of 5-15 minutes. What's even weirder, is that sometimes, if I power cycle the device, it'll jump up by 30-60%. But then just dies again in another 5-15 minutes.
And there's a screenshot after I just power-cycled.
It jumped from 11% to 71%!!
I've also tried letting it get to 5% then charging it to 100%, done that twice. No luck. I don't know if this is related, but if I power it completely off, and plug it in, it turns on... kinda weird. My Note 3 doesn't do that, it just stays off and shows the battery charge indicator.