Six crew members on board the 180-ton French boat Monbijou were rescued by helicopter 20 miles off Dungeness, on the French side of the Channel.
But Dover Coastguard, which helped with the operation, said the search for the seventh crew member had ended.
It said the boat ran into difficulties in "horrendous" conditions on Friday.
'Minimal hope'
A spotter plane and the British tug boat Anglian Monarch were involved in a cross-Channel search from first light on Saturday.
A spokesman for Dover Coastguard said: "The search has been called off because there is minimal hope of finding him. It won't resume. The trawler is semi-submerged but it is too stormy for recovery to be made.
"It will probably take a day or two to sink fully and in the meantime we are broadcasting navigation warnings to passing vessels to make them aware of the trawler."
He said the partly submerged boat posed little pollution risk as it was carrying only a small amount of diesel.
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