Phillip assumes that his father and other men in boats are searching for him in The Cay, but what does he fail to understand?
Phillip believes that the most likely way of being rescued is to remain on the raft so that they can be found by boats or planes flying overhead. But the boy fails to realize that perhaps no one is searching for him--that all survivors of his sunken ship have already been rescued and no search is underway. Phillip and Timothy have drifted for hundreds of miles into an area rarely visited by ships. Phillip also neglects to understand that if his ship can be sunk by German U-boats, then any search vessels would also be put in jeopardy. It is only much later that Phillip discovers that
... a war was on and all the ships and aircraft were needed to fight the U-boats. (Chapter 8)
No one was out looking for Phillip because there were far more important uses for any available ships or airplanes.