CHESTERFIELD, Mo.  In 2005, Jim Lynch placed a big bet on a big vehicle.

He was already a successful Hummer dealer, but he spent $7.5 million on a new 34,000-square-foot showroom in a wealthy suburb of St. Louis. He even turned 60 acres of Missouri River flood plain into a rough-terrain test track, with visions of people coming from afar to try, and buy, his brawny sport utility vehicles.

General Motors cheered him on, he says, telling him he could eventually sell as many as 1,300 Hummers a year  which start at more than $30,000 and can cost more than $100,000, not to mention the thousands that many owners spend on accessories  more than enough to cover his monthly mortgage payment of $60,000. He sold 70 new Hummers a month when he opened the store, but now sees only a handful of customers each month. “That doesn’t even pay the interest on my inventory,” Mr. Lynch said. “Now I’m lying awake at night trying to think of what I can do with this big, beautiful building.”

Sales of Hummers over all have fallen so far  51 percent last year, the worst drop in the industry  that General Motors is trying to find a buyer for the brand. Without one, the company might close Hummer. An announcement about Hummer’s fate may be made Tuesday.

“It’s a brand that represents a lot of what people want to get away from,” said Rebecca Lindland, an analyst with the research firm I.H.S. Global Insight.