It found by majority verdict that another claim was not defamatory and another was defamatory, but not of Hagaman. It was unable to decide whether the remaining three instances were defamatory.
Lani Hagaman had also claimed she was defamed on the same six occasions, but the jury found by majority verdict that she was not.
Though Hagaman has died since the trial, Lani Hagaman is pursuing a retrial on his behalf.
She took a case to the Court of Appeal, where the parties argued whether the challenge could survive Mr Hagaman's death.
The Court of Appeal ruled that it did not and Lani Hagaman then sought leave to take the case to the Supreme Court.
Justices Sian Elias, Mark O'Regan and Ellen France, in a decision released this afternoon, declined to take the case.
Lani Hagaman, in applying for leave, said that the law should be interpreted to allow appeals in defamation cases because the challenge becomes a cause of action vested for the benefit of the deceased's estate.
"We do not see this argument as having sufficient prospects of success to justify the grant of leave," the three judges said.
Hagaman's representatives were ordered to pay $2500 in costs to Little.