Despite Facebook (NASDAQ:FB) shares hitting an all-time high just days ago, many investors are not happy. Not because the stock hasn't performed well, but because Facebook continues to have glaring corporate governance pitfalls and they're frustrated with CEO Mark Zuckerberg's lack of accountability.

The social media juggernaut's annual shareholder meeting last month merely served as a reminder that His Zuckness exerts complete control over the company, as the shareholder proposal to eliminate Facebook's supervoting Class B share class was easily struck down (again). An overwhelming 83% of independent investors voted in favor of that proposal.

Mark Zuckerberg on stage beneath Facebook's visualization of a connected world

Image source: Facebook.

Some institutional investors aren't giving up the fight, though.

"He is not accountable to anyone"

Business Insider reports that numerous investors that collectively hold about $3 billion in Facebook shares continue to fight the company's corporate governance structure. That includes institutional shareholders like a New York City pension fund manager, the Illinois state treasurer, and various capital management firms, including one (Trillium Asset Management) that manages the investments of a philanthropic organization.

Trillium was the shareholder at this year's annual meeting that put forth the proposal calling for a risk oversight committee, which was shot down. In a symbolic concession to investors, Facebook's board did incrementally empower its audit committee by giving it more responsibilities with risk oversight, although these fell short of Trillium's formal proposal.

"He is not accountable to anyone, not the board or the shareholders, which is a bad corporate governance practice," the Illinois state treasurer, Michael Frerichs, told BI. "He's his own boss, and it has clearly not been working."

This is really the crux of the issue. In January, Zuck argued that Facebook's board of directors is "the group that ultimately governs Facebook," but that's laughable. Making that proclamation is borderline insulting for sophisticated investors that realize Zuck wields 60% voting power, in which case he can singlehandedly vote any director in or out. Zuck answers to the board, which answers to Zuck. There are no checks and balances.

Desperate times call for desperate measures

Facebook investors should check out the BI report, but the reality of the situation is that Zuckerberg has to voluntarily agree to any outcome that improves Facebook's corporate governance structure. Remember that early on he scored a then-unprecedented deal with private investors that granted him unparalleled authority and control, a precedent that ended up paving the way for other comparable arrangements.

Activist investors can continue fighting, but without Zuckerberg's consent, there is literally nothing anyone can do about it. What's less clear is what could actually jolt Zuckerberg into appreciating the benefits of good corporate governance, as undermining the issue has helped make him one of the wealthiest men in the world.

It's a Catch-22, since investors' only recourse is to sell shares in protest. In doing so, they send a message, but also risk missing out on potential gains. Fundamentally, the scandals have only reinforced the advertising business, which will help support the stock price.

The worst-case scenario for investors is that a cratering stock price is the only thing that gets through to Zuck, which would not only jeopardize his personal net worth, but his philanthropic efforts and the legacy he leaves behind for his children. There's no end in sight for Facebook's ongoing corporate governance travesties.

Evan Niu, CFA owns shares of Facebook. The Motley Fool owns shares of and recommends Facebook. The Motley Fool has a disclosure policy.