Austrian adventurer Felix Baumgartner has been frustrated in his attempt to make the highest ever skydive.
Unfavourable winds at Roswell, New Mexico, have prevented the launch of the helium balloon that was to take him to more than 120,000ft (36.5km).
Meteorologists say Thursday now looks to be his best bet for a record bid.
Baumgartner - famous for jumping off skyscrapers - is hoping to become the first human to break the sound barrier unaided by a vehicle.
Because of the rarity of the atmosphere at 120,000ft, he would accelerate rapidly once he stepped out of his balloon's capsule.
Calculations suggest he could achieve Mach 1 - thought to be around 690mph (1,110km/h) at the target altitude - within 40 seconds.
But this will all have to wait for another day.
Baumgartner's 30 million cu ft (850,000 cu m) polyethylene balloon has very strict launch requirements.
Wind speeds from the ground up to about 800ft (250m) must not exceed 3mph (5km/h), or there is a chance the envelope could shred as the support team try to release it.
And although Tuesday morning's conditions at the surface were dead calm, the winds about 700ft up (215m) at times were just too gusty.
Felix Baumgartner got as far as climbing into his capsule before the mission was postponed.
The latest weather intelligence had suggested there would be a good window to get airborne, but as the balloon filled, a sudden 25mph (40km/h) blast of air twisted the fragile envelope.
That could have damaged the thin skin of the balloon and so flight controllers felt they had no option but to abort.
"There was nothing we could do," said team meteorologist Don Day. "Once you put helium in that balloon, it's like a big sail."
The current weather window for this year probably extends for another month. Beyond that and the team will likely have to return next year.
"The further you go into Fall, the less opportunity you have," said Day.
"Thursday's a good possibility. Is it as good a possibility as we saw today? Maybe not. But what it comes down to is whether or not we can have a long enough time of light winds. And right now we see that as a good possibility on Thursday, but we're not in a position to make that call right now."
The team promises an update at 0900 local time (1500GMT; 1600BST) on Wednesday.
A major consideration is that the group now has only one more of the special helium balloons in reserve.
Once unpacked, these colossal envelopes have to be used or binned, which makes the decision to go for another launch on Thursday all the more pressured.
"There's a lot riding on the next time," conceded project director Art Thompson. "So the big thing for us is making sure the probabilities are very high - that we have a very good launch window."
Baumgartner is trying to topple records that have stood for more than 50 years.
The previous highest skydive was made by retired US Air Force Col Joe Kittinger, who leapt from a helium envelope in 1960. His altitude was 102,800ft (31.3km).
The adventurer first discussed seriously the idea of taking on the challenge in 2005.
Since then, he has had to battle technical and budgetary setbacks to make it happen.
What he is trying to do is extremely dangerous.
At an altitude of 120,000ft (36.5km), the air pressure is less than 2% of what it is at sea level, and it is impossible to breathe without an oxygen supply.
Others who have tried to break the records for the highest, fastest and longest freefalls have lost their lives in the process.
Baumgartner's team has built him a special pressurised capsule to protect him on the way up, and for his descent he will wear a next generation, full pressure suit made by the same company that prepares the flight suits of astronauts.
Heated sun visor
Oxygen supply hose
Main parachute handle
HD camera on each leg
Suit made of layered material
Mirror to check parachute
High altitude balloon: expands with altitude
Balloon made of plastic film 0.002cm thick
Frame attaches capsule to balloon
Sliding door to exit capsule
Foam insulated shell
Although the jump has the appearance of another Baumgartner stunt, his team has stressed its high scientific relevance.
The researchers on the Red Bull Stratos project say it has already provided invaluable data for the development of high-performance, high-altitude parachute systems, and that the lessons learned will inform the development of new ideas for emergency evacuation from vehicles, such as spacecraft, passing through the stratosphere.
Nasa and its spacecraft manufacturers have asked to be kept informed.
Jonathan.Amos-INTERNET@bbc.co.uk and follow me on Twitter: @BBCAmos