At the Corcoran, they call it “the three c’s”: a museum agenda focused on the collection, the college and the community. But what is easily summarized with a neat, alliterative mnemonic does not, in practice, always yield a coherent identity.

Looking back over a decade or more of exhibitions at the Corcoran Gallery of Art gives one a dizzying sense of how widely the institution defines its mission. Shows of student work and work by faculty at the Corcoran’s art school jostle with populist fare such as a 2002 exhibition about Jacqueline Kennedy and photography shows devoted to Richard Avedon and Annie Liebowitz. In between were some memorable and important exhibitions that explored substantial themes and bodies of work, including the 2010 Eadweard Muybridge photography show and the huge and rewarding 2007 exhibition “Modernism: Designing a New World,” with which , then the Corcoran’s director, hoped to reboot the institution after the 2005 disappointment of canceling a major addition project by Frank Gehry.

Add it up, the hits and misses, the controversial exhibitions that seemed designed to court and flatter collectors rather than woo audiences, the flat-out embarrassments — such as the 2003 show devoted to J. Seward Johnson Jr.’s sculpture (excoriated by former Post art critic Blake Gopnik as the worst museum exhibition he had ever seen) — and you get a sense not just of an institution serving many masters, but an institution responding honestly but erratically to the myriad and often fractious currents in the art world today.

And then there was Mapplethorpe.

The cancellation of a 1989 show of Robert Mapplethorpe’s homoerotic photography still haunts the museum, as much as they would like to put it in the past, as much as they have tried to repair the damage and not blunder into similar controversies. As the art world once again discusses the fate of the museum — the board of directors is currently considering selling the 1897 museum building and decamping for a new location — it is the Mapplethorpe exhibition that is almost invariably chosen as the beginning of the institution’s long trail of woe.

“It fractured the board of trustees in a significant way,” said Philip Brookman, chief curator and head of research at the Corcoran Gallery of Art. Brookman wasn’t at the Corcoran when the Mapplethorpe controversy exploded during the height of the debate about public funding of art and the role of the National Endowment for the Arts. He was at the Washington Project for the Arts, which stepped in and hosted the exhibition after political pressure from homophobic Sen. Jesse Helms and other culture warriors affrighted the Corcoran’s leadership.

“More important,” said Brookman, “it damaged the Corcoran’s reputation in the museum world. I think that still exists.” Still, Brookman doesn’t want to dwell there.

“I wish we could get past it.”

When case studies are written about how to blow up a nonprofit institution, the Mapplethorpe controversy is key among them, a classic map that prefigured controversies such as the implosion earlier this year at the breast cancer charity Susan G. Komen for the Cure (which suddenly appeared political after trying to deny funding to Planned Parenthood), the 2010 censorship of an exhibition of gay and lesbian portraiture at the Smithsonian’s National Portrait Gallery, and the current power struggle at the University of Virginia. In all four cases, institutional leadership seemed unaware of the basic human capital invested in the organization, unaware that the people who keep the institution alive view it in essentially familial terms, not bureaucratic or organizational ones.

And so a decision made from the top wasn’t just unpopular, but perceived as peremptory, dictatorial and disenfranchising, and the result was a cascading sense of betrayal and alienation. In all four cases, the base of the organization reacted not with a dispassionate weighing of self-interest, but with the kind of family feud intensity that keeps grievances fresh for decades.

That, in some ways, may be the basic institutional problem of the Corcoran: It serves a collection of Corcoran families (local artists, students, art lovers looking for something more experimental than what is offered at more institutional museums), which is a source of strength, and often an impediment to focusing its mission. It has, like all institutions, made mistakes along the way, but for some reason it hasn’t been able to capitalize on the things it does right. Every wrong turn advanced it further toward isolation, dark progress that for some reason wasn’t remedied by many right turns. People stopped listening; donors turned away; audiences drifted elsewhere. And now, no matter what it does, it doesn’t get the credit it deserves when it does something right.

A case in point is the current exhibition devoted to the paintings of Richard Diebenkorn. It’s a very fine show, it looks spectacular in the Corcoran’s galleries and it demonstrates how vital the Corcoran can be if it remains focused on something missing from “the three c’s”: the city’s serious audience for art. Yet at a critical moment, when the Corcoran desperately needs people to rally behind it, the board of directors has indicated that it is seriously considering a move that would further alienate supporters of the museum. Board Chairman Harry Hopper, in an interview with Washington Post reporters, said he and the board “weren’t out pounding the pavement on behalf of the institution” until they have “a plan that makes sense.”

So even if a wildly successful Diebenkorn show prompted a flood of support for the institution, it’s not clear that it could be marshaled to preserve and build the Corcoran, another instance of the goodwill engendered by successful programming being squandered by leadership without vision. The Corcoran’s idealistic agenda focused on the community, the college and the collection is now in danger of being whittled down to just the college, leaving the collection without a landmark home, and the community again wondering what its relationship to the institution should and will be.