By Chris Isidore, CNN Business

(CNN) -- Elon Musk is a visionary and enjoys a cult following among many of Tesla's customers. But he is a loose cannon as a CEO of a company with public investors.

Now he is once again battling the Securities and Exchange Commission, which could seek to strip him of his position at Tesla.

The SEC on Monday asked a federal court to find Musk in contempt for violating a settlement agreement reached in October. Musk tweeted last week that Tesla would build 500,000 cars this year. That was incorrect: Tesla has said it would only produce about 400,000 cars during the year. Musk had not received Tesla's approval to send his tweet. That violates the agreement, according to the SEC.

The regulator didn't specify what penalties it will seek if he is found in contempt, but it had previously sought to remove Musk as CEO. Last year, Musk falsely tweeted that he had secured funding to take the company private. In the October settlement, the SEC allowed Musk to keep his CEO job, but he agreed to give up his board chairman position. He also needed to get pre-approval from Tesla's laywers of social media posts about company information that is "material" to investors.

The decision on whether to remove Musk as CEO doesn't rest with the SEC; it would be up to a judge. Or Tesla's board could decide to pull the plug on Musk, if it decides it has had enough.

Musk is a loose cannon

Musk is undoubtedly the genius behind the industry-changing electric cars Tesla builds. But he is also the driving force behind the volatility in Tesla's stock and the revolving door of top executive talent at the company.

For example, Tesla's top lawyer quit a day after Musk's February 19 tweet that got him into trouble with the SEC. Last year Tesla's chief accounting officer left after less than a month in the job following his "funding secured" tweet. The company has also lost top engineers.

Yet Musk has shown no remorse. He continued to tweet about his dislike for the SEC after the court filing, saying, "Something is broken with SEC oversight."

Even Tesla bulls are starting to shake their heads.

"We expect the debate of whether Tesla is better off without Musk will return," said tech analyst Gene Munster, managing partner of Loup Ventures, in a blog post.

"Musk's behavior remains careless," Munster wrote. "In this case, the tweet wasn't as careless as the disrespect for the process he agreed to in the October settlement."

Munster's comments are particularly biting, because Munster is a longtime Musk supporter.

Musk seems reasonably well insulated from getting thrown out of his own company. He hand-picked the board, including his brother, fellow billionaire Larry Ellison and the company's new chairwoman.

A Tesla spokesman declined to comment.

Musk a mixed bag for Tesla

Munster said the company has reason to consider a new CEO.

If Musk leaves, Tesla would more easily recruit and maintain senior management. It would reduce the volatility for the stock. Tesla's stock fell 3% Tuesday.

In a note to investors, Wedbush analyst Daniel Ives said he remains "concerned around this issue being another distraction for Musk & Co. as the company navigates one of its most challenging periods in its history and certainty did not need this news."

Musk's antics are a distraction for the company. As many hours as he spends at Tesla, sometimes sleeping at the plant, he has two other companies he is also leading — SpaceX and the Boring Company.

But Munster believes that Musk is irreplaceable. Staying with Tesla would be a net positive for the company. His product vision, focus on pace of innovation and delivering great customer experiences are not easily replicated.

The execution of that vision has often fallen short. Tesla is famous for missing deadlines and targets. And last week Consumer Reports, which has loved its cars during road tests conducted by its staff, again stripped one of its cars, the Model 3, of its "recommended" rating due to reliability and maintenance problems reported by Tesla owners in surveys.

Still, Tesla's current owners are among Musk's biggest fans. Consumer Reports says that despite maintenance problems, customers are more satisfied with their purchase than the owners of any other car brand. Customers treat Musk like a rockstar. That's one of the reason why the question of whether Musk will stay or go is such an important one.