Post-Modernist buildings, those teasing, colorful mash-ups of columns, pilasters and pediments, were both praised and reviled in the 1970s and ’80s, their heyday. But by the end of the ’80s they fell out of fashion, consigned with surprising abruptness to the dustbin of architectural history. In 1988, at the paradigm-shifting “Deconstructivist Architecture” show at the Museum of Modern Art, Michael Graves, one of America’s pre-eminent Post-Modernists, observed, “I’m toast.”

Or so it seemed. In the fickle turn of architecture’s style wheel, some of the complex architectural collages that once challenged Modernism’s cool, geometric simplicity are now enjoying a Lazarus moment, including works by Mr. Graves and Philip Johnson. Others, such as the 1996 addition to the Museum of Contemporary Art San Diego, in La Jolla, by the postmodern pioneers Robert Venturi and Denise Scott Brown, are facing demolition rather than resurrection.

Heading into their fourth and fifth decades, deep into midlife architectural crises, needing face-lifts, they’re now vulnerable and back again in the public eye, eliciting concern and attracting a second look — and sympathy — even from people who never liked them. But will these loved-hated structures be saved, and should they?