The Opportunity robot lost contact with Earth on Monday, leading scientists to believe it has entered "lower power fault mode" - or gone to sleep.
The robot relies on sunlight to power its solar panels and charge its batteries.
But the Martian dust storm, first detected on May 30, has continued to grow and now blankets a quarter of the Red Planet.
The team are now operating under the assumption that the charge in Opportunity's batteries has dipped below 24 volts and it has gone to sleep, NASA said in a statement.
"The rover has entered low power fault mode, a condition where all subsystems, except a mission clock, are turned off," it added.
The mission clock is programmed to wake the computer up so it can check power levels.
However, if the computer determines that the rover's batteries do not have enough charge, Opportunity will put itself back to sleep leaving engineers unable to contact it.
Due to the extreme amount of dust over Opportunity, engineers are concerned that the rover will not have enough sunlight to charge back up for "at least the next several days".
If the rover is unable to charge back up again, it may lose contact with Earth, bringing an end to a 15-year mission that gave scientists an unprecedented look at the Martian service.
The rover has already proved hardier than expected by lasting nearly 15 years - despite being designed for a 90-day mission.
This is not the first time Opportunity has hunkered down in bad weather.
In 2007, a much larger storm covered the planet leading to two weeks of minimal operations, including several days with no contact from the rover to save power.