So it sounds like you are talking about one of the scenes from Flags of our Fathers the one about the flag raising on Mount Suribachi on Iwo Jima.

And as morbid as it might be to say, the convoy itself isn't going to stop for one dumb Marine who fell over. Nor is the ship itself going to risk a collision or falling behind by trying to come out of line amongst dozens or hundreds of other ships and try to stop and lower boats or nets/ropes to recover and then try to catch up. In part because of time concerns, but also greatly because of the risk of submarine attacks. Japanese and German subs remained a threat until the last days of the war, as the Indianapolis can attest. For a slow whale of a cargo ship, keeping moving and altering course in a zig-zag were basically their only defense and the whole ship is simply more important than one man. While the escort screen of light warship might be in a position to help they also have their jobs to do looking for subs and other threats and would generally be several hundred yards or more out from the convoy itself.

Not that isn't to say a man overboard is instantly dead, small task forces or single ships often did and do stop to recover or search for them. And in other situations precautions were taken. A carrier conducting flight ops for instance would have a destroyer just behind it and off slightly to the side as a plane guard. Its job would be to scoop up any air crew who ended up in the water while landing or taking off from the carrier. But it was also expressly assigned to that job, and wouldn't leave a whole in the CV's screen by stopping, and was fast enough to catch up to the others and could defend itself well. But when you have dozens and dozens of wallowing transports the issues with stopping even a single one and causing a traffic jam.