As it struggles to ramp up production of its make-or-break mass-market electric car, Tesla has launched a companywide reorganization that will flatten its management structure, CEO Elon Musk told employees Monday.

One problem: There’s less and less structure to flatten.

A stream of top managers has left the Palo Alto automaker in recent months or stepped aside from their duties. This includes, most recently, a key safety executive, who departed for a rival company even as a federal investigation continues into the fatal crash of a Tesla using self-steering Autopilot software on Highway 101 this spring. (In another crash last week in Utah, a Tesla smashed into a stopped fire truck at about 60 mph; the driver said she was using Autopilot mode and had been looking at her phone, according to the Associated Press.)

In his brief email to employees Monday, Musk did not address the executive departures, which also include top managers of engineering, finance and Autopilot. Instead, he emphasized that Tesla would continue to add staff connected to production of the Model 3, the $35,000 sedan considered the linchpin of Tesla’s plans. Tesla employed 37,543 people worldwide at the start of the year, and the company has been hiring at its Fremont auto factory.

“As part of the reorg, we are flattening the management structure to improve communication, combining functions where sensible and trimming activities that are not vital to the success of our mission,” Musk wrote. “To be clear, we will continue to hire rapidly in critical hourly and salaried positions to support the Model 3 production ramp and future product development.”

Bloomberg reported last week that Tesla’s vice president of engineering, Doug Field, would take a sabbatical but remain with the company. Matthew Schwall, director of field performance engineering and the company’s main technical contact with such federal agencies as the National Transportation Safety Board, left Tesla for self-driving rival Waymo, a sister company of Google, according to the Wall Street Journal.

Jim Keller, head of the Autopilot program, left for a position at Intel in April. Corporate Treasurer and Vice President of Finance Susan Repo left in March. So did Chief Accounting Officer Eric Branderiz.

The number of recent departures and the names involved have raised eyebrows, even though Tesla has experienced churn almost since its founding nearly 15 years ago.

Musk, known as a demanding boss even in less-mission-critical times, has been pushing hard to increase production of the Model 3 to 5,000 cars per week by the end of the current quarter. He tweeted Sunday afternoon that a hackathon was under way to fix the two worst automated choke points in the car’s production process, which he has already described as too heavily automated. He has also emphasized the overall safety of Autopilot while playing down the recent crashes, tweeting Monday that the focus on the Utah crash, in which the driver seems to have escaped with just a broken foot, was “super messed up.”

“He’s definitely difficult to work with, and that can burn people out,” said Efraim Levy, senior equity analyst at the CFRA research firm. “And there’s a lot of stress internally with the Model 3 that may be pushing people out.”

The on-leave Field was one of only four top executives named in Tesla’s most recent shareholder proxy statement, along with Musk, Chief Financial Officer Deepak Ahuja and Chief Technology Officer J.B. Straubel.

“When you see executive turnover at high levels at crucial times — like with the Model 3 — it’s disconcerting,” Levy said.

Musk had previewed the reorganization to Wall Street analysts early this month, saying a management restructuring would help the upstart automaker finally achieve profitability. He predicted that Tesla, which lost a record $784.6 million in its most recent quarter, would turn a profit in this year’s third and fourth quarters.

While Tesla investors appear to be most focused on Model 3 production, the executive departures have raised questions, as did Musk’s at-times-combative performance during the company’s most recent earnings conference call. Tesla stock dropped 3 percent Monday to close at $291.97.

David R. Baker is a San Francisco Chronicle staff writer. Email: dbaker@sfchronicle.com Twitter: @DavidBakerSF