Eva Rose Stevens weighed just over 2lbs and lived for just 52 minutes after she and her twin sister, Dottie Mae, were born at 26 weeks and four days in December.
Dottie Mae remains in the Neonatal and Intensive Care Unit (NICU) at Burnley General Hospital.
She still only weighs 2lbs and doctors have warned restaurant supervisor Kerry Parker (32) and her partner, Simon Stevens, she will remain in hospital for at least another two months, up to the date when she was due.
The twins, who were due in March, arrived on December 15th after Kerry's waters broke while she was at the home of her sister, Gemma Braithwaite.
Kerry, who works at the Three Millstones in West Bradford, was rushed to hospital and doctors were able to give her steroids to help the twins' lungs mature ready for when they were born 12 hours later.
Touched by the devastating blow to the family, who live in Clitheroe, well wishers have donated £2,026 to the fund set up by Gemma. The money is to help pay for a headstone for Eva Rose and also the numerous costs associated with hospital visits.
Simon, who has a son Olly (nine) has returned to his job as a plastic welder at Ultraframe in Clitheroe but Kerry travels over to the hospital every day and, as she doesn't drive, she often has to get the bus if Gemma or the people who have offered lifts, are not able to take her.
Gemma said: "It has been an incredibly difficult and sad time for the family with so many mixed emotions but the staff, doctors and midwives at Burnley have been amazing and so supportive and kind and people have been so generous with their donations."
Kerry and Simon, who is originally from Hapton, were given the chance, along with the other members of the family, to spend time with Eva Rose and say goodbye to her in the serenity suite at the hospital.
Gemma also praised staff at Clitheroe Funeral Home for the 'exceptional' care and support shown to the family.
If you would like to make a donation to the fund please click HERE