Jet fuel is known as the Steady Eddie of the refinery business, a predictable profit maker that balances the seasonal gyrations of gasoline and diesel sales. But for airlines, it is a headache — a big and unpredictable expense that confounds managers. So Delta Air Lines tried a bold experiment: It bought an oil refinery in 2012 outside Philadelphia, the first such purchase by a major U.S. airline. When jet fuel prices were high, as they were then, Delta figured the refinery, which turns crude oil into the stuff that planes, cars and trucks burn, could offset some of its expenses and perhaps even make money.

“A lot of energy guys hate it, and I can understand why, because we’re taking money out of their pockets,” Ed Bastian, the airline’s current chief executive and then president, said at an industry conference in 2012. But the refinery made only modest profits some years and lost money in others. This year, as the coronavirus hammered demand for air travel, it has become a liability for Delta, widely considered by analysts as one of the best-run airlines in the country.

The energy industry critics Mr. Bastian dismissed appear to have correctly identified the flaws in Delta’s strategy. Like airlines, oil refining is a cyclical enterprise that can be difficult in the best of times — refineries are expensive to run, prone to accidents and subject to environmental regulations, yet earn meager profits.

Today, airlines and refineries face their biggest crises in modern times. Tens of millions of people are working from home, and the number of people flying is down about 75 percent from a year ago. Delta’s refinery, Monroe Energy, has been one of many casualties in an industry that is working well below capacity, idling plants, and losing money.

Monroe, in Trainer, Pa., lost $114 million in the second quarter, and its future appears bleak. In 2018, Delta announced that it was interested in finding a partner to jointly own and operate it, but it never found any takers.