Bluetooth lives next to USB 3 in the spectrum, and USB 3 leaks. When the Switch is docked, the dock ports, TV, and nearby gadgets put out extra hash that a controller has to punch through. That is why handheld mode feels fine but the couch is flaky.
You can attack it three ways. Remove noise by moving drives and hubs and pushing Wi Fi to 5 gigahertz. Improve the link by bringing the dock out in the open. Or skip radio by turning on wired communication for the Pro Controller and using a cable. Any of those will break the every few minutes drop pattern.
