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It bears mentioning that in season one, episode eight ("Good-Bye Island"), they did in fact try to fix the Minnow with a miracle glue that Gilligan discovered, but in the end the glue turned out to be highly unstable and the entire boat ended up flying into pieces at the end of the episode.

So it's not that the Professor couldn't fix a hole in the hull - he would have had to rebuild the entire boat from scratch, which is a considerably bigger task. And the Professor is often criticized for not at least building a raft or smaller boat, but that ignores the fact that in season one, episode one ("Two On a Raft") Gilligan and the Skipper did attempt to reach the shipping lanes on a raft, only to discover that the prevailing currents in the area would return any such small craft directly to the island.

A historical note: the glue that Gilligan discovered in this episode is NOT the same glue which was used to repair the lens on the satellite camera that crashed on the island, setting off a chain of events in which the castaways ended up convincing NASA that Mars was populated by bird-people.