The house that Kevin Hargrove built with the help of Habitat for Humanity volunteers had everything he wanted for his family: It was in the same New Orleans neighborhood where he’d grown up, with plenty of space for his daughters. A charity had donated furnishings, so as soon as the construction was finished, they stepped inside and it felt like home.

But another aspect felt even more important: The $550 he owed every month was not rent but a mortgage payment. The house would truly be his, something he could hand down to his daughters. “Building generational blessings,” as he put it.

More than a decade later, though, the pistachio-green house with the shutters and big front porch that Mr. Hargrave believed would be his legacy is now in serious danger of being taken away. A blizzard of letters remind him of what he already knows: He is behind enough in his payments to be eligible for foreclosure.

The cost of the property insurance that his mortgage agreement with Habitat requires has soared in the past couple of years. That, in turn, has pumped up his payments significantly — to $1,735 a month. He can’t afford that, he said, no matter how many extra shifts he picks up at the warehouse where he works.

“I shouldn’t be having to do this,” Mr. Hargrove, 55, said of the juggling act his finances have become as he asks for extensions for some bills and does not pay the full amount for others. “What more do I need to do?”

The situation has been held up as a dire warning for other homeowners across the state: Insurance premiums will most likely keep rising as a changing climate threatens more frequent and intense natural disasters in Louisiana, which is particularly vulnerable, and many other states.