WASHINGTON — Representative Kevin Cramer, Republican of North Dakota, said on Thursday that he would not challenge the Democratic incumbent senator, Heidi Heitkamp, in this year’s midterm elections. It was just the latest indication of the difficulty Republicans are having recruiting candidates in what had looked to be a highly favorable climate in the wake of President Trump’s inauguration a year ago.

Ms. Heitkamp is among 10 Democrats seeking re-election in states won by Mr. Trump in his race against Hillary Clinton in 2016. Mr. Cramer had been seen as a top-tier challenger in a state the president carried by 36 percentage points. He made his announcement during a North Dakota radio program.

“This is shaping up to be a tough cycle for Republicans across the board,” said Jennifer Duffy, a senior editor for The Cook Political Report who specializes in Senate races. “It only makes sense that recruiting is going to be difficult. For someone like Cramer, it doesn’t make a lot of sense to give up a safe seat for a difficult race in a lousy environment.”

That assessment is an abrupt reversal of how most analysts saw the midterm landscape shaping up a year ago.