Kim was with him when his stay of execution was last granted.
Rodney Reed's appeal against his death sentence will not be heard by the Supreme Court.
Justice Sonia Sotomayor announced on Monday she was denying his petition for a review of his murder case; however she did not "close the door" on future appeals pending upcoming hearings in the lower courts.
The now 51-year-old Reed has spent more than 20 years on death row after being convicted of the 1996 murder of 19-year-old Stacey Stites.
Stites' body was found raped, sodomized, strangled and partially burned in her home town of Bastrop, Texas; DNA from saliva and semen was found to match Reed.
After his arrest, Reed initially claimed not to have known the victim; however he later claimed they were having an affair, but didn't want to admit it because Stites was white, engaged to a local police officer, and they were in the South.
Reed appealed his conviction nine times, unsuccessfully, on grounds that witnesses were ignored and evidence was dismissed, such as the belt used to strangle the victim never being tested for DNA, and forensic experts later admitting mistakes in their testimony.
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His case was taken up by the Innocence Project, and attracted the attention of many celebrities, including Kim Kardashian, Rihanna, Beyoncé, Susan Sarandon, Oprah Winfrey and Meek Mill.
In November, Kim revealed she was with him when his stay of execution was granted — just five days before he was due to be put to death.
"Words cannot describe the relief and hope that swept over the room in that moment," she wrote at the time, praising everyone who had spoken up in his defense, "all because of a deep belief that every man or woman accused of a crime - especially one punishable by death - deserves the chance to have all available evidence considered."
In her decision, Justice Sotomayor said Reed's petition "has presented a substantial body of evidence that, if true, casts doubt on the veracity and scientific validity of the evidence on which Reed's conviction rests."
"Misgivings this ponderous should not be brushed aside even in the least consequential of criminal cases; certainly they deserve sober consideration when a capital conviction and sentence hang in the balance," she wrote.
"While the Court today declines to review the instant petition, it of course does not pass on the merits of Reed's innocence or close the door to future review," she added.
"I remain hopeful that available state processes will take care to ensure full and fair consideration of Reed's innocence."