After reading some replies on here, there seem to be a lot of various theories. I'm sorry if it doesn't work for you, but I can confirm that exiting Steam worked for me. The problem is very repeatable.
- Connect and disconnect controller
- Sleep and wake up system
- Xbox One Wireless controller connects (as shown in the "Game Controllers" panel) and disconnects within 2 seconds.
- Exit Steam
- Xbox One Wireless controller connects and works.
- Restart Steam (controller still works)
- Disconnect Xbox One Wireless controller, then connects and disconnects within 2 seconds.
I'm narrowing my problem down to the Big Picture mode, so that problem is for another forum...
Hopefully this workaround helps a few people before the real solution is found.