So, first day when I got my Touch controllers, they worked fine.
Next day, they didn't turn on, and I had to take the batteries out to reboot them.
Next day I got my third sensor, and the controllers worked fine.
Today they didn't turn on, and I had to take the batteries out to reboot them.
Could this be some weird Bluetooth problem, because they're on a shelf about six feet away from the headset when I boot the PC and don't receive a command to turn on?
Last night they worked, but I made sure to have them near the headset when I turned the PC on. I'll try to some more tests and see if I can figure out when they work and when they don't, then let the support folks know if I find a way to reproduce it.