Wireless controllers disconnecting

I have two wireless controllers for my XBOX ONE, and they both began exhibiting the same issue at the same exact time: neither will stay connected to the console for more than about a minute. They will briefly act normal and be able to control the OS or
game, but then the gem starts flashing and the console complains that I need to reconnect and press A. Several seconds later the flashing ceases and I can press buttons to continue playing. This cycle continues until I get fed up and turn the system off. I
can only play games by streaming to my PC, using a wired XBOX 360 controller.

I have turned my XBOX ONE off, even disconnecting its power brick to ensure it wasn't just in low power mode. I have changed the batteries to use every combination of rechargable and/or alkaline AA that I have in my house. I have attempted to update their
firmware (no update available). They work perfectly when I connect them to the console with a USB cable, but my longest cable is 3ft and I'm not going to sit on the floor and strain my neck. Using the sync buttons on the controllers/console improves nothing.

The XBOX Support page has a Wireless Controller Troubleshooter, which doesn't help and says that my controllers need to be replaced. But why would two controllers, purchased at different times (one is the blue Forza controller), both begin showing the same
issue on the same day and hour?

:)