I had an issue on my own Xbox One where one or other controller would randomly disconnect and then reconnect few seconds later after pressing A button on the affected controller. After ruling out obvious issues (low batteries, wireless interference, re-pairing, updating firmware), I started looking into hardware.
Original Xbox One Controllers communicate using proprietary Wi-Fi Direct type of connection (newer models added Bluetooth for PC connection, but controller to console connection is still using Wi-Fi). Specific part that manages Xbox One wireless communications is shown below and can be easily find to buy online my searching Xbox One Wireless Board 1525.
This board doesn't cost much (around £15 for a refurbished one). I just bought one online and replaced using brilliant iFixit instructions. That was it! After re-pairing controllers connection now was rock solid without any further disconnections.
Microsoft Wireless Board 1525