Winning a death row appeal might get even tougher without Justice Anthony Kennedy serving as the swing vote on the U.S. Supreme Court.

“If a death row prisoner was going to obtain relief from his conviction or death sentence, most of the time he would need Justice Kennedy’s vote,” Robert Dunham, executive director of the Death Penalty Information Center in Washington, told Bloomberg Law.

Kennedy, who’s retiring in July and could be replaced by a more reliable conservative from President Donald J. Trump’s shortlist of candidates, has played “an important role in developing and enforcing constitutional protections for persons...