New York (CNN Business) How much longer will the 737 Max be grounded? No one really knows.

Boeing insists it is making progress on getting its fix for the troubled jet approved by the US Federal Aviation Administration, which it needs to put the Max back in the air. But the company has stopped giving any public estimates about when that approval might come.

The fatal crash of an Ethiopian Airlines plane that prompted the grounding happened three months ago this week. At the time, Boeing extended condolences to the family members of the victims and said it expected a fix "in the coming weeks." That software fix is designed to address the plane's automatic safety feature, which is the focus of the investigation into the Ethiopian Airlines crash and another crash involving a Max flown by Lion Air in Indonesia last year.

Those weeks came and went. After the FAA said in early April that additional work would be needed , Boeing again suggested it would be only a short delay and said the fix would be "completed in the coming weeks."

Months later, it's clear the initial time frame proved far too optimistic.

Asked Tuesday for the latest estimate for a return to service for the 737 Max, neither Boeing nor the FAA could give a time frame.

Boeing said it is now providing additional information to address FAA requests that include detail on how pilots interact with the airplane controls and displays in different flight scenarios. Once that process is complete, it will work with the FAA to schedule a certification test flight and complete certification paperwork.

What's more, even after the FAA does approve a fix, Boeing will face the challenge of getting approval from more than 30 other airline regulators around the world. Those international regulators will have to be convinced that both Boeing and the FAA got it right this time.

"The technical fix is relatively simple compared to the political difficulties," said Richard Aboulafia, aerospace analyst with The Teal Group. "The need and difficulty is to get everyone on same page, and to assure international regulators."

American Airlines AAL United UAL Southwest Airlines LUV Airlines that have the 737 Max in their fleet now aren't expecting the planes back until August at the earliest. On Sunday canceled flights on its schedule through Labor Day.andhave canceled flights through early August.

Aboulafia said he believes FAA approval is likely to come in August, though he won't be shocked if the process takes more time. As it is, when the grounding itself was first announced, he never expected it to last this long.

Will the plane be back in the air before the end of 2019? That's what Boeing CEO Dennis Muilenburg was asked last week on CNBC -- and he was notably vague.

"I do," he replied. "But again, I can't give you the specific timeline on it."

Muilenburg continues to insist the plane will be among the safest in the air when it is allowed back into service. He has personally flown on some of the flights that tested the software fix.

has also admitted that it will take sometime to But Muilenberghas also admitted that it will take sometime to win back public trust in the company and the plane.

sold the plane with a promise that pilots who were already trained on the standard versions of the 737 would be able to fly the 737 Max. If the FAA makes the determination that pilots need more training for the Max, that could delay the ability to return the planes to service. Part of the question that the FAA will consider is how much additional training pilots will need before flying the 737 Max. Boeing originallysold the plane with a promise that pilots who were already trained on the standard versions of the 737 would be able to fly the 737 Max. If the FAA makes the determinationthat pilots need more training for the Max, that could delay the ability to return the planes to service.

has not been grounded. Further complicating the issue is news that parts of the wings of both the 737 Max and the earlier versions of the jets, the 737 NG jets, need to be inspected . But those types of inspection orders are relatively common in the industry, and the 737 NGhas not been grounded.

Though the process of approving the plane could take a while, experts still say the Max could be back in service before the completion of the investigations of the causes of the Ethiopian Airlines and Lion Air crashes.

Those probes typically take a year or more to complete, according to Bill Waldock, a professor of aviation safety and director of the crash lab at Embry-Riddle Aeronautical University. So even the Lion Air crash investigation likely won't be completed for another five or six months.

"I don't see that being completed by [this] summer. The fall is more likely," Waldock said.

The crash investigation is being done by safety authorities in Ethiopia and Indonesia, with the participation of the US National Transportation Safety Board. The FAA does not conduct crash investigations, and its findings on the proposed fix for the 737 Max will be independent of the probes.