Shirley Long, 77, was admitted to hospital with breathing difficulties after two men forced their way into her house in Manchester Road and stole cash, bank cards and a mobile phone on Sunday, November 17.
She died in hospital on Wednesday night.
Det Chief Inspector Nick Wallen, who is leading the investigation, said: “Mrs Long was a frail and vulnerable member of the community and clearly she never recovered from this heartless attack.
“The men who robbed her committed a cowardly and despicable crime and need to be swiftly brought to justice. That’s why we are again calling for anyone with information to come forward.”
Two men from Bradford, both aged 37, were arrested on suspicion of robbery and remain on bail.
Anyone with information is asked to contact police on 101 or Crimestoppers on 0800 555111.