The spacecraft, the oldest of five NASA robotic explorers studying Mars, was circling the planet snapping high-resolution images and studying the climate in a mission that led to the first evidence that water once flowed on the planet's surface.
The Global Surveyor went silent after reporting problems with a sticky solar panel, and scans of the skies have produced no sign of it.
"MGS was a fantastic mission. It has really revolutionized how we look at Mars," Fuk Li, Mars Exploration Program manager told reporters. "We haven't given up hope, but we are all ready to celebrate a long life and a job well done."
One chance remained on Tuesday to recover the probe, which has been programmed to transmit a signal to NASA's robotic geology station, Opportunity, located near Mars' equator.
Opportunity will relay any signal from the orbiter to Earth during passes on Tuesday and Wednesday via the Mars Odyssey.
"If MGS is in the sky and its (transmitter) is on, then Opportunity should receive it," John Callas, project manager for the Mars Exploration Rover mission, said.
Scientists at NASA's Jet Propulsion Laboratory in Pasadena, Calif., lost contact with the spacecraft on November 2 after it signaled it was having trouble moving one of its solar panels to track the sun as it emerged from behind Mars.
The spacecraft is programmed to position itself so that a stuck panel faces the sun, but that orientation could block its communication with mission controllers, Tom Thorpe, the Mars Global Surveyor project manager said.
If Mars Global Surveyor is turned away from the sun for more than a few orbits it could be low on power, an outcome that seemed to be supported by the spacecraft's apparent failure to respond to commands that would raise its transmitter, Thorpe said.
"We don't believe the (solar) panel is in any way degraded...The problem seems to be the gimble motor that is sticking," Thorpe said. "Why we can't raise the transmitter could be a function of the power problem."
Mission scientists first hailed the orbiter via the Deep Space Network, receiving what they believed was a weak carrier signal from the probe two or three days into the search. Then it went silent.
They then turned to the newly arrived Mars Reconnaissance Orbiter, which used its onboard cameras on Friday and Monday during passes near Mars Global Surveyor's last known orbit. But that probe had no definitive sightings of its sister craft.
If Opportunity records no sign of Mars Global Surveyor, scientists said they will have exhausted the most likely possibilities for contacting it.
The 10-year mission, which was extended four times, cost a relatively modest $377 million.
Mars Global Surveyor's cameras were the first to record topographic features suggesting flowing water on Mars, and its magnometer found the remains of magnetic fields that once shielded Mars' surface from deadly cosmic rays.
Its mineral mapping helped scientists choose landing sites for Opportunity and its twin, Spirit, and will be used to evaluate landing sites for the next-generation of Mars surface probes, the Phoenix and the Mars Science Laboratory.