When Donald J. Trump made an appearance this spring at the New York Military Academy, his high school alma mater in Cornwall-on-Hudson, he spoke of it with gratitude and in glowing terms, describing it as “one of the really great military academies.”

“I had such incredible experiences here,” Mr. Trump told a crowd during a campaign stop in April.

But six years ago, when it was on the verge of closing under the weight of debt, and a small group from the school came to Trump Tower seeking financial assistance, Mr. Trump gave a swift and firm response: No.

“We were disappointed,” said Rich Pezzullo, an alumnus who attended the meeting, which took place as Mr. Trump was participating in an online real estate auction and ended when the winner of his Miss USA pageant showed up. “We thought he’d open up his checkbook,” Mr. Pezzullo said.

Over the years, Mr. Trump has billed himself as an “ardent philanthropist,” and his official biography says that he is “involved with numerous civic and charitable organizations.”