U.S. home prices rose steadily upward in February as more homebuyers chased fewer available properties, a trend that many analysts say may not be sustainable.

The Standard & Poor’s CoreLogic Case-Shiller national home price index, released Tuesday , increased 5.8 percent in February, the most in 32 months. Such strong price gains and slightly higher mortgage rates may eventually cool off demand.

But for now, sales of new and existing homes are robust. Last month, sales of existing homes reached their highest level in a decade. The strong demand, however, hasn’t enticed more Americans to sell their homes. The number of houses for sale has dropped to its lowest level in nearly 20 years, which makes finding an available home the toughest challenge awaiting potential buyers in the spring home buying season.

Many homeowners have benefited from the sharp price gains of recent years, but those increases have also made