The Scottish Ambulance Service is now looking into the incident and has apologised for the anguish caused to the woman, who called for medical assistance after a fall in her home.
The woman, who asked not to be named, has a rare genetic condition called Ehlers-Danlos syndrome, which affects the connective tissues supporting the organs and bones.
As a result, she had endured numerous gruelling surgical procedures over the years, including knee and ankle joint reconstructions.
She also experiences joint dislocations far more often than normal, and was left in agony after falling on Tuesday afternoon.
Her sister today called on the Scottish Ambulance Service to investigate to find out why her family member was left in pain as her condition rapidly worsened over the four-and-a-half-hour wait.
Her sister said: “Because of her condition she can dislocate something just getting up off the couch, getting up, getting dressed, or getting tea.
"She does remarkably well. “She really self manages it so well, that people wouldn’t know what she’s going through.
"On Tuesday afternoon she dislocated her knee while walking through to the kitchen at about 4.45pm and called the ambulance.
"Sometimes it can be popped back in quickly because of her condition, and the quicker that happens the less pain she’ll be in and she can recover quicker.
"But if it’s left too long it can start to seize up and it means the recovery will be longer.
"Initially she told us not to come round as she’d already called the ambulance and they’d be there any minute.
“Because of her frequent injuries, the ambulance folk know her on first-name terms. The paramedics are amazing.
"If they're quick enough, they can relocate joint and she won’t even need to go to hospital."
But on this occasion things didn’t go so swiftly. A few hours later the ambulance still hadn’t arrived, and her condition had deteriorated.
"She called again at 8pm, and told them pins and needles and was losing the feeling in her leg, which is really worrying. They told her she was a top priority.
“But she was still waiting two hours after that.
“She called again just after 10pm and they said she was next on the list. About 20 minutes later they arrived.
“We’ve logged a complaint. We need to be able to rely on this service, and we need assurances that this is going to be looked at.
“We just can’t accept someone lying for four and a half hours with a dislocated knee. It can’t happen again.”
A Scottish Ambulance spokesperson apologised for the delay, saying: “While we are limited in what we can say due to patient confidentiality, we can confirm we received a call on Tuesday, April 6, which was initially triaged as non-immediately life threatening.
"At the time of this incident we were experiencing exceptionally high demand in the Lothian area and our crews were working hard to help our sickest patients.
"We would like to apologise for the wait this patient experienced and we will be reviewing this incident thoroughly to identify any learnings.”