The Brooklyn Academy of Music has long struggled to maintain fiscal solvency in the face of slack attendance and an underfunded endowment, but in recent years, BAM has begun a turnaround that will culminate this fall with the completion of an $8.6 million restoration. In addition, the academy has announced two major gifts totalling $30 million, which will double the size of its endowment. Still, the organization’s long-term success seems to be inextricably tied to the fortunes of Brooklyn as a whole.