Tesla CEO Elon Musk, already facing an SEC investigation that started when he tweeted about taking his company private, has continued to tweet -- despite being asked by his board not to.

On Tuesday, he disputed a recent newspaper article about him and reprised unfounded claims about a Thai cave-rescue diver that are currently the subject of a pending lawsuit. And on Wednesday came news that the National Labor Relations Board has filed a complaint alleging Musk broke U.S. labor laws when he tweeted in May about a union organizing effort at Tesla's Fremont, California, plant.

In response to discussion of a New York Times profile that depicted the CEO as stressed, working 120-hour weeks and alternating "between laughter and tears," Musk replied: I wasn't crying.

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"For the record, my voice cracked once during the NY Times article. That's it. There were no tears," he tweeted.

Soon after, a Twitter user reminded Musk about the time he accused Vernon Unsworth, a British rescue diver working to rescue the trapped Thai soccer team, of being a pedophile. (Musk first lobbed the unfounded accusations in July, then apologized for them and deleted those tweets.)

But on Tuesday, he inexplicably returned to that argument.

"You don't think it's strange he hasn't sued me?" Musk tweeted, referring to the diver.

"Did you investigate [the accusations] at all?" Musk later tweeted. "I'm guessing answer is no. Why?"

Some hours later, Unsworth's lawyer replied to the tweet with a picture of a letter sent to Musk informing him he would be sued for libel.

Musk's behavior has mystified even his fans. One investor on Wednesday asked him to lay off Twitter. Besides the embarrassment, bad Twitter behavior could have consequences for Musk's company, Wired editor Nick Thompson told CBSN.

"If Musk ends up facing severe consequences, or perhaps has to give up his position, it's terrible for Tesla," Thompson said. "The only reason Tesla is able to support itself and is able to get funded at such an extraordinary level despite losing gobs of money is because people have so much faith in Musk."

"His board has asked him to get off Twitter. And to start taking everything a little more seriously," Thompson continued. "He needs to settle down, run his companies and keep quiet for a while."