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Proposals to require labels for foods containing genetically modified ingredients so far have a spotty record at the ballot box. Another defeat arrived Tuesday in St. Louis, this time at the annual shareholder meeting of Monsanto Co.

Investors in the GMO seed maker overwhelmingly rejected a shareholder proposal that would have pushed Monsanto to get behind labeling efforts itself – after it spent millions lobbying against such measures at the state level. Only about 4% of Monsanto shares were voted in support of the effort.

The shoot-the-moon proposal did, however, bring Monsanto Chief Executive Hugh Grant to personally debate some fierce critics of his company’s business practices – something he acknowledged Monsanto hasn’t done much of in the past.

“We simply haven’t engaged enough at the level we should have with all of our audiences, and for that, we apologize,” Mr. Grant said at the meeting. “There’s a recognition we need to do more.”

As anti-GMO protesters rallied near the event among cars festooned with giant, grinning vegetables, Mr. Grant got his chance at such engagement. He faced critiques during the meeting from a handful of consumer advocates who derided the company for promoting pesticide use and using its influence to shroud food origins in mystery. The advocates said they represented owners of Monsanto stock.

Shareholder efforts to wrangle Monsanto’s support for GMO labeling come as advocates of such measures battle state-to-state against agricultural and packaged-food companies, which have argued that such measures will raise the cost of food and unfairly give the impression that crops grown with genetics designed to withstand weedkillers and pesticides are not safe.

New Hampshire legislators last week became the latest state to reject such a measure, following the defeat of a highly contentious ballot initiative in Washington state in November. Maine and Connecticut, meanwhile, in recent months have passed laws requiring such labels, though these don’t go into effect until other states approve similar measures. Proposals are pending in other states as well.