SK advice from Feb 17 2016 worked for my iPad mini 3.
“This is definitely a weird problem. Especially given that in joshthegeek’s case, after draining the battery completely it still doesn’t work. Here’s a tip that you can try and let us know if it works for you. Instead of the lock button to power down, we will try to power down the device in another way.
Go to Settings > General > Accessibility. Tap on the Assistivetouch and Turn it on . you will see a circle thingy appear. Tap on it. On the next pop-up menu tap on Device. Press and hold on the option for “Lock Screen” and you should see the Slide to Power Off dialog appear. Slide to turn off the device. Please report back if it works.”