Question: I know there is a good reason but, if the castaways could build huts, bicycle powered generators and fix the radio, why couldn't they fix the boat?
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Answer: There's no absolute answer to this, but: 1) The hole in the boat was big enough that they couldn't patch it sufficiently well to float it. All the rafts, huts and other constructions on the island, were flimsy enough that wind and rain got through most of them reasonably easily. 2) None of them were qualified to build or repair boats, so it would have been risky to even try going out with a patch they made. 3) It's a silly 60's sitcom - making sense was never a big concern of producers at the time!
DavidRTurner