Brian Harmon had just finished spending over $300,000 to fix his home in Kingwood, Texas, when Hurricane Harvey sent floodwaters “completely over the roof.”

The six-bedroom house, which has an indoor swimming pool, sits along the San Jacinto River. It has flooded 22 times since 1979, making it one of the most flood-damaged properties in the country.

Between 1979 and 2015, government records show the federal flood insurance program paid out more than $1.8 million to rebuild the house—a property that Mr. Harmon figured was worth $600,000 to $800,000 before Harvey hit late last month.

“It’s my investment,” the 49-year-old said this summer, before the hurricane. “I can’t just throw it away.”

In years past, he had considered a buyout from local officials seeking to purchase often-flooded properties. Now, he finally wants to get out. “I never want to go through this again,” said Mr. Harmon, who bought the house in 1995.

As they tally up the losses from Hurricanes Harvey and Irma, government officials are looking for ways to step up purchases of frequently-flooded houses, which have become a huge drain on the financially troubled federal flood insurance program.

Homes and other properties with repetitive flood losses account for just 2% of the roughly 1.5 million properties that currently have flood insurance, according to government estimates. But such properties have accounted for about 30% of flood claims paid over the program’s history.

Can the federal government afford to insure homes that face repeated flooding? Already roughly $25 billion in debt, the National Flood Insurance Program is facing massive new claims following hurricanes Irma and Harvey. WSJ's Shelby Holliday reports. Photo: Getty

“We are seeing a very acute need to move far faster” on property buyouts, said Roy Wright, who directs the National Flood Insurance Program. “It’s a clear priority to address these multiple-loss properties.”

In a buyout program, homes are typically razed and the land left as open space.

Even before Harvey and Irma, the flood program owed the U.S. Treasury $24.6 billion, as payouts have exceeded the amount of insurance premiums it takes in.

The program paid out more than $47 billion in insurance claims since 2000, according to government figures.

Insurance payouts from Harvey alone are expected to total $11 billion, said Mr. Wright, noting the program had already received nearly 85,000 claims tied to the disaster as of Wednesday. It is too early to estimate losses tied to Irma, but Mr. Wright expects both storms to be among the most costly in the program’s history.

Florida and Texas, the two states hit hardest by the back-to-back disasters, are home to nearly one in five of the most frequently flooded properties, according to an analysis of federal flood insurance data by the Natural Resources Defense Council, an advocacy group that supports increased buyouts.

Nearly half of frequently flooded properties in the U.S. have received more in total damage payments than the flood program’s estimate of what the homes are worth, according to the group’s calculations.

“Anyone looking at this would say there are perverse incentives for staying on the floodplain,” said Nicholas Pinter, a geology professor and associate director of the Center for Watershed Sciences at the University of California, Davis, who has analyzed repeatedly flooded properties.

Mr. Wright said he has “no authority to cancel policies, none at all” when homes suffer multiple losses. The agency can, however, put “folks who have multiple losses in a position where they have the opportunity to move on rather than simply re-establish them in harm’s way” by buying these homes with federal funds, he said, and is looking at ways to expedite the buyout process.

Purchasing such homes can be cheaper for the government in the long run than repairing and rebuilding, flood experts say. But government efforts have been hampered by limited funding, long delays and the reluctance of homeowners—and sometimes communities—to participate in buyout programs.

Kingwood neighborhood along the San Jacinto River in Texas. Aerial image taken in January 2017. Published Credit: Pictometry Photo: Pictometry

Satellite imagery taken before and after Hurricane Harvey. Illustration: Digital Globe

Richard Smith, who lives near Cypress Creek northwest of Houston and has flood insurance, said his two-story elevated house has flooded six times since 1994 and took on more than 60 inches of water after Harvey.

“We will be thinking very seriously about a buyout,” said the 82-year-old retired contracts manager, who lives on a fixed income. But “where do we go?” He said one consideration, beyond whether a buyout offer is sufficient, is that staying in the neighborhood would allow Mr. Smith’s grandson to live with him while attending college nearby.

Speeding up the buyout process is among the first steps that need to be taken to reduce flood risks, said Ed Emmett, the top elected official for Harris County, which includes Houston. Local officials have requested $800 million to buy properties that can’t otherwise be remediated because they are so deep in the floodplain or where a buyout is more cost effective.

Both the Federal Emergency Management Agency and the Department of Housing and Urban Development fund buyouts.

Some flood experts say the government needs to do more. “The number of repeatedly flooded properties is growing much faster than our efforts to mitigate those properties,” said Robert Moore, a senior policy analyst with the NRDC. He believes the flood program should pre-qualify homeowners with flood insurance for a voluntary buyout if their home is substantially damaged in a future disaster.

In Florida alone, 808 properties were the subject of at least five flood insurance claims between 1978 and 2011, according to a paper published this summer by coastal researchers Juliano Calil of the Center for the Blue Economy and Sarah Newkirk of the Nature Conservancy.

In the Houston area, the Harris County Flood Control Department last year identified 3,300 structures as candidates for its buyout program. Under federal requirements, property owners must volunteer for a buyout.

As of Wednesday, 1,850 property owners had asked to join Harris County’s program following Harvey, well above the dozen or so requests in a typical month. It isn’t clear how many will meet the agency’s criteria, which include the cost effectiveness of a buyout, the depth of flooding, the risk to homeowners and first responders and whether there are other, more appropriate ways to reduce flood risk.

“If we had funding right now, we would be able to capture many more volunteers than we will would be able to capture six months from now,” said James Wade, manager of the Property Acquisition Department, which runs the county flood district’s buyout program.

Six employees are now fielding inquiries, up from two prior to the storm, along with help from the communications staff. “These are properties that should never have been built to begin with,” he said.

Funding for buyouts is limited and the process can be cumbersome as it works it way between local requests, state reviews and federal approvals. “Unfortunately, the process takes two to 2 1/2 years,” long enough for many homeowners to make repairs and change their minds, said Larry Larson, senior policy adviser for the Association of State Floodplain Managers.

Homeowners aren’t the only ones who can get cold feet. Some communities are reluctant to offer buyouts because funding is limited and the program removes properties from their tax base, said Delton Schwalls, an engineer in Orlando who works with Florida communities on flood mitigation.

Jeff Brandes, a Republican state senator who represents Pinellas County, Fla., this fall for the third time introduced legislation that would use $50 million in state environmental funds for buyouts and other mitigation efforts. “So much of this is driven by federal incentive dollars,” he said. “States are not wanting to use general-revenue dollars to purchase single-family homes so they can tear them down.”

Some communities believe there are more effective ways to reduce flood risk. Over the last three years, St. Petersburg, Fla., has used federal funding to help seven residents elevate or tear down and rebuild their homes, said Chief Building Administrator Rick Dunn.

The city had 362 properties with repetitive flood losses at the start of 2017, but believes it is more cost effective to take such steps to make a property safer and compliant with flood codes.

The terms and effectiveness of buyout programs vary, with some programs targeting individual homeowners, while others aim to relocate entire neighborhoods. “Every entity is designing this as they go,” said Alex Greer, an assistant professor at Oklahoma State University who studied buyouts after superstorm Sandy. “Policy should iterate over time and get better,” he added. “When you look at buyouts, it isn’t that.”

—Shelby Holliday and Jim Oberman contributed to this article.

Write to Ruth Simon at ruth.simon@wsj.com