Looking forward to Lincoln Center’s namesake festival this summer? It’s been scrapped. Good luck finding the center’s new Hall of Fame that was promised a few years ago: on the back burner. And those long-delayed plans to radically remake the home of the New York Philharmonic? Being rethought.

Now on its fourth leader in five years, Lincoln Center — the country’s largest performing arts complex — finds itself suffering from shuffled priorities, financial difficulties and instability at its highest rank during a time when cultural organizations are struggling to retain and build donors and audiences.

“It just feels like the whole place hasn’t come together around what they need,” said Karen Brooks Hopkins, the longtime former president of the Brooklyn Academy of Music, and an expert in arts management. “A lot of things are changing in the field — the pressure on them is intense.”

The center’s troubles erupted into public view in April when its most recent president, Debora L. Spar, left after only a year on the job. Though her departure was described at the time as a mutual parting of ways, recent interviews made clear that she was pushed out after a rocky tenure.