MONTPELIER, Vt. — To those close to the legal wrangling over the Vermont Yankee nuclear plant or standing on the sidelines, it’s becoming clearer that the state’s lone reactor will survive its 40th birthday two weeks away.

The administration of Gov. Peter Shumlin, who has led the charge to close the plant when its license expires March 21, acknowledged as much in papers filed Wednesday with state utility regulators.

Vermont Law School Professor Patrick Parenteau, who has followed and blogged about the legal issues surrounding Vermont Yankee, put the chances that the plant’s critics will succeed in shutting it down this month at “about zero.”

Even a lawyer for the New England Coalition on Nuclear Pollution, which has fought the plant since before it split its first atoms in 1972, gave less than even odds that Vermont Yankee would close in March.

“It’s possible, but I don’t know about likely,” coalition lawyer Jared Margolis said.

Vermont Yankee won a 20-year extension of its federal license a year ago, after a five-year review by the U.S. Nuclear Regulatory Commission. The permit it needs from the state, where nuclear skeptics have come to populate the governor’s office and Legislature, has been another story.

The state Senate defeated a measure that would have given the Public Service Board the OK to issue Vermont Yankee a permit in 2010. Vermont Yankee owner Entergy Corp. sued in U.S. District Court, and a federal judge in Brattleboro ruled in January that lawmakers had overstepped their authority. He sent the question of the permit, or “certificate of public good,” back to the Public Service Board.

The Senate’s action came a month after it was revealed that radioactive tritium was leaking from underground pipes into soil and groundwater surrounding the plant and that Vermont Yankee officials had misled the board and lawmakers by saying the plant didn’t have the sort of underground piping that carried tritium.

The board isn’t expected to issue a decision on the permit for several months, and Vermont Yankee is expected to continue operating in the interim, lawyers said Wednesday.

The board generated excitement among Vermont Yankee’s critics, and consternation among its backers, in late February when it issued a series of questions to lawyers for Entergy, the state and anti-nuclear groups that appeared to raise the possibility the plant might have to close March 21.

But the Department of Public Service, which represents the governor and consumers before the board, said in legal papers Wednesday that it doesn’t see any way the state could force the shutdown without violating the Jan. 19 ruling by U.S. District Judge J. Garvan Murtha.

The DPS commissioner, Elizabeth Miller, wrote in an email that her department believes the board must proceed for now with its permit review in accordance with the judge’s ruling.

If Vermont Yankee were to shut down this month or later this year, Vermont and New England electric consumers most likely would not miss it, said Michael Dworkin, a former Public Service Board director of the Institute for Energy and the Environment.

“The New England (electricity) market has significant excess capacity,” Dworkin said, adding that likely would be the case “for at least five years and probably longer.”

He said Vermont Yankee power is not essential to the reliability of the grid.

March 21 marks the end of existing contracts under which Vermont Yankee has been selling power to Vermont’s two major utilities. Lawyers for New Orleans-based Entergy argue in papers filed with the board that even without the contracts, the plant will have a big economic impact on the state. About 650 people work at the plant, and it pays millions of dollars a year in taxes.

Raymond Shadis, technical adviser with the New England Coalition, said in an interview that Vermont Yankee and the Entergy-owned Pilgrim plant in Plymouth, Mass., “continue to stagger on,” a decade or more after other New England nuclear plants dating from the late ’60s and early ’70s are no longer operating.

“They’re living on borrowed time,” Shadis said.