The previous bids to bring the piece of wreckage, estimated to be at least 10 meters (33 feet) long, out of the water failed after lines being used to lift it broke, according to Indonesian authorities.
On Saturday, sharp parts of debris sliced through a strap. On Sunday, a wire rope snapped after the fuselage had reached the surface of the water.
The military divers were hoping to avoid similar problems Monday by using twice as much rope as the day before, said Suryadi B. Supriyadi, director of operations and training for Indonesia's search and rescue agency. They were also putting the inflatable bags being used to lift the wreckage inside the fuselage, he said.
But the deteriorating weather conditions halted the efforts, Supriyadi said later Monday.
Officials are aiming to float the wreckage to the surface and then hoist it onto a waiting ship.
Flight QZ8501 went down on December 28 as it flew from the Indonesian city of Surabaya toward Singapore with 162 people on board.
Indonesian officials have said they believe many of the remains of people still missing from the disaster may be inside the fuselage.
Supriyadi warned that the walls of the plane body are broken and move around easily, making the divers' task harder.
They had successfully carried out a similar procedure with the tail section of the aircraft earlier this month.
As the fuselage neared the surface on Sunday, one body appeared in the water and was retrieved, authorities said. It's the 70th recovered so far during weeks of searching.
Efforts by divers before the weekend to examine and get inside the fuselage as it lay on the seafloor were hindered by strong currents and bad visibility. Bad weather repeatedly interrupted the work to try to lift the plane over the weekend.
Investigators are analyzing the contents of Flight QZ8501's flight data recorder and cockpit voice recorder as they try to establish why the Airbus A320-200 went down in an area of heavy thunderstorms.
Experts have speculated from the outset that the storms might have played a role
in the plane crash.
The aircraft lost contact with air traffic control after the pilot asked permission to turn and climb to higher altitude because of bad weather, officials have said.
Indonesia's transportation minister said Tuesday that Flight QZ8501 climbed rapidly, and then stalled
shortly before it crashed.