Over the weekend, the tech entrepreneur caught flak for tweeting an unfounded accusation that one of the divers who helped rescue 12 boys from a Thai cave is a pedophile. He has since deleted the tweet.
The Tesla CEO made the comment at a precarious time for the company, which has struggled to bring the Model 3, its mainstream vehicle, to market. Bottlenecks have severely delayed the delivery timeline Musk promised for the Model 3, and Tesla may need to raise more money from investors soon to avoid a cash crunch.
Musk's comments could dissuade shoppers from buying a Tesla, said Rebecca Lindland, an analyst with Kelly Blue Book. That could hurt sales, and ultimately anger investors.
"When you're looking to expand the appeal of your product beyond innovators themselves, beyond early adopters ... you've got to be careful," said Lindland. "You've got to start acting like a CEO."
A big, public company like Tesla isn't only valued by its earnings but also the behavior of the chairman and CEO, Lindland noted.
Musk is "not showing the kind of discipline of someone going to manufacture hundreds of thousands of cars," said Brian Tierney, CEO of Brian Communications.
Tierney said someone close to Musk should tell him: "Put down the phone, let's just focus."
Musk is no stranger to controversy.
The outspoken CEO has criticized the press and jeered analysts. But accusing someone of pedophilia "seems over the top, even for him," said Bryan Reber, department head at the University of Georgia's communications school.
Spokesmen for Tesla and Musk's other companies, SpaceX and Boring Co., did not respond to requests for comment.
The latest controversy began when the diver, Vernon Unsworth, criticized Musk's attempt to help save the stranded boys with a "kid-size submarine." Many of Musk's supporters admire his desire to solve complicated problems. But that quality can work against him.
"He is attracted to problem-solving and yet, at the same time, he's distracted from problems that aren't yet solved in his own company," Lindland said.
Just last week, one of Tesla's biggest investors called for the CEO to stay out of trouble.
"We think a time of quiet and peace is what is needed to work through these [production] issues," James Anderson, a partner at Tesla's fourth largest investor, Baillie Gifford & Co., said in a Bloomberg Television interview on Wednesday.
"I think that it would be good to just concentrate on the core task," he added.
Anderson told the Guardian that he plans to talk to Musk this week about the latest controversy. Anderson declined to comment for this story through a spokesperson.
Shares of the company slumped 3.5% on Monday. But the small dip probably isn't enough to scare investors away, said Reber. "They've been pretty loyal ... I suspect it's going to take a pretty dramatic drop," to change that.
Ronn Torossian, CEO of the public relations agency 5WPR, thinks the controversy will blow over.
"He's lashed out before, this isn't the fist time," Torossian said of Musk. "A week from now, people won't remember this."