Mrs Rainey, who was in her 50s, was found in a burning car at her Knockloughrim home and rushed to hospital in the early hours of Tuesday morning.
She later died from her injuries.
A PSNI spokesperson said: “Detectives from the Police Service of Northern Ireland’s Major Investigation Team, investigating the murder of a woman in Knockloughrim on 12 October, have been granted a further extension of 36 hours to question a 59-year-old man arrested on suspicion of murder.”
Previously PSNI Det Chief Insp John Caldwell said hospital staff had battled hard to save Ms Rainey but she ‘succumbed to her injuries and died in hospital’.
“A 59-year-old man has been arrested on suspicion of murder. He has also been taken to hospital for treatment for burn injuries,” he said.
“My investigation is at a very early stage and I would appeal to anyone who was on the Quarry Road early this morning and who witnessed anything to contact detectives.”
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