MARTINSBURG, W.Va.—Bernie Sanders defeated front-runner Hillary Clinton in West Virginia on Tuesday, regaining momentum and leaving some of Mrs. Clinton’s backers uneasy that her path to the Democratic presidential nomination figures to be rocky to the end.

“I’m always uncomfortable when she loses,” said New Hampshire state Sen. Lou D’Allesandro, a Clinton supporter. “Every time [Mr. Sanders] presents himself and presents his story, more people start talking about him. And that goes on and on.”

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