The rabbit's revenge for having its foot removed.
The Baron said:
Gilligan's Living Doll:
A robot parachutes onto the island, and the castaways try to figure out a way to use it to get them off the island. The robot is reasonably well-conceived - about the level of a "Tenth Planet" - era Cyberman.
I strongly suspect that the title of this episode is a gag on the 1964-65 series My Living Doll, which is not much remembered now, but would've been current when this episode was released.
Back Story: The robot was Model XR-1000. It was being carried on an unmanned drone plane for Hickam Field to Vandenberg AFB on a radiation detection flight when it was accidentally ejected.
Taking It Seriously: I think we have to assume that robotics is somewhat more advanced in the Schwartzverse. The robot claims to be programmed to buld a carrier, destroyer or minesweeper - it is also programmed to construct a toy schooner.
Considering this is apparently one of the most advanced robots in the world, the Professor seems to be able to reprogram it awfully easily.
Gilligan Spoils A Rescue: Yes. The castaways determine that the robot is able to walk to Hawaii. They give it a message to deliver to the authorities. However, Gilligan places his rabbit's foot charm into the robot's interior to bring it luck, and the charm somehow
reverses the polarity of the neutron flowdemagnetizes the receptor spools and hopelessly garbles the castaways' message.