It might seem like a great time to own apartment buildings.

For many landlords, it is. Rents have soared in recent years because of housing shortages across much of the country and a bout of severe inflation.

But a growing number of rental properties, especially in the South and the Southwest, are in financial distress. Only some have stopped making payments on their mortgages, but analysts worry that as many as 20% of all loans on apartment properties could be at risk of default.

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Although rents surged during the pandemic, the rise has stalled in recent months. In many parts of the country, rents are starting to fall. Interest rates, ratcheted higher by the Federal Reserve to combat…