Drones carry their own power source - usually a LiPo battery.
What you're proposing would not work if the phaser could just keep firing (which seems likely). Onboard AI seems the solution (assuming the Faraday cage is effective enough, which remains to be seen).
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.
Source: I flew UAVs "drones" for the US Army for 482 combat flight hours in Iraq. Lookup the wikipedia for "Ground Control Station" for an old pic of an 18 year old me @ the UAV training center "black tower" in Ft Huachuca, AZ.