> Drones carry their own power source - usually a LiPo battery.
You misunderstood me. Use that to provide power to the antenna which is outside the Faraday cage, and the battery is inside.
> What you're proposing would not work if the phaser could just keep firing
The phaser has a range though. So program the drone to fly up and away if it gets hit (no need for AI to do that). Then reactivate communication and stay away from the phaser area.