I literally went through this last night.
Suddenly, for no apparent reason (no update), neither of my controllers would 'wake up' or pair. They both unpaired, but once unpaired, I couldn't re-pair. I tried everything many, many times. Brand new batteries, hold the meta button + Y, hold X and tap the meta button five times, etc. Nothing worked. They appeared unresponsive, but the lights work, and a 'pointer' seems to work but not do anything. The pointer moves with each controller, implying a connection of some kind.
So, last ditch effort, a factory reset.
When I ended-up at the controller pairing screen, I could do nothing. I'm hosed! Tried changing batteries a few times, hoping it might 'wake' them. Nothing.
At one point, with the battery out, I noticed three little contact points that are hidden behind the battery, when the battery is in the controller. Interesting. Why have three contact points that contact nothing? Maybe for special rechargeable batteries that I've never heard of? Doubtful there's a battery with side contact points.
I swiped my finger across the three contact points and the controller woke up and paired. Did the same with the other controller, and now I'm back up and running, reinstalling my games/apps (I don't seem to remember my backup pin number :( )