The payoff can be worth a few nerve-wracking months. Some new stores, birthed as seasonal Hamptons shops, have been able to score long-term success. Athletic-wear shop Bandier, which started as a single summer store that opened in Southampton in 2014, has expanded to six full-time locations, including a flagship store on New York's Fifth Avenue. Bandier's Hamptons location looks different from its other shops, which are emporiums of stretchy pants and performance tops meant for the spin studio or barre class. It's filled with items it doesn't sell elsewhere—sunglasses, swimsuits, cosmetics, clothes for golf and tennis. The Hamptons shop continues to shut down during the off months, and hosts pop-ups for other labels, such as a trunk show for Reebok.

"Originally, I thought I'd open in New York," said founder Jennifer Bandier. "But the rents were so high."

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