Bluetooth Keyboard and mouse disconnect when idle for a few seconds and reconnects when moved / typed on Ubuntu 20.04
Solution 1:
You didn't make it clear if you'd gone through the GUI and power settings, so I'll take a stab at this.
Open your power settings and disable the ability to suspend Bluetooth devices to save power.
Solution 2:
Increase the IdleTimeout in /etc/bluetooth/input.conf or set it to 0 to disable it.
You can also try setting FastConnectable to true in /etc/bluetooth/main.conf to allow the devices to reconnect faster at the trade off of increased power consumption.
Restart blue tooth after any changes: sudo service bluetooth restart