Mr Fossett, the first person to fly solo around the world in a hot air balloon, vanished on September 3 after taking off from a private airstrip in Nevada.
Dozens of planes have spent the weeks since scouring areas of remote desert, hunting for traces of the aviator and his light aircraft.
But with no clue to the 63-year-old whereabouts, the search team's daily sweeps over Nevada's rugged terrain have now been halted.
Volunteers are expected to continue checking Google Earth's satellite maps for signs of any potential crash sites.
If they spot any credible leads, Nevada Civil Air Patrol aircraft will respond on an "as-needed, on call basis".
Mr Fossett went missing while scouting for locations for a planned land-speed record. He had not filed a flight plan, and his emergency tracking beacon was never activated.
The adventurer set 115 world records in balloons, aircraft, sailboats, gliders and airships, including his 2002 hot air balloon circumnavigation of the globe.
Three years later, in March 2005, he became the first person to fly a plane solo around the world without refuelling.
Mr Fossett was inducted into the US's National Aviation Hall of Fame in July, vowing to continue flying.
"I'm hoping you didn't give me this award because you think my career is complete, because I'm not done," he told the crowd.
A tireless athlete, Mr Fossett swam the English Channel, raced in an Ironman Triathlon and climbed mountains including the Matterhorn and Mount Kilimanjaro.
He took part in the gruelling 1,887km Iditarod Trail Sled Dog Race across Alaska, as well as the 24-hour Le Mans auto race.
He survived numerous brushes with death, near-misses and crash-landings, including a 9,000m plummet into the Coral Sea off Australia when his hot air balloon was shredded in a storm.