The six-foot bird - named Ethel - fled its home last Thursday after being spooked by passers-by taking its photograph.
The bird, which is native to Australia, has now been spotted on more than a dozen occasions in parks all across Doncaster but has so far eluded capture.
When approached Ethel, who can run at speeds of up to 30mph, has out-paced its would be human captors.
There have also been reports of gangs of local youths pelting the terrified bird with stones.
Today the bird's owner Kerry Dobson put out a desperate appeal to get her feathery pal back home after she suddenly escaped from their property in Doncaster.
Kerry, who is originally from Sheffield, said: “She's terrified. She’s been running since Thursday so could be anywhere. She's had stones thrown at her and all sorts, she's not used to being out she must be terrified.
"I’m aware of all the sightings Thursday and Friday. I need to know of more recent sightings on Saturday and Sunday.
“We are in contact with the police and RSPCA but had no luck catching her; she just ran further. They couldn't catch her. She was so scared she just kept running."
Both South Yorkshire Police and the RSPCA have been bombarded with calls about the bird.
A police spokesman said: “The last sightings suggested it was heading back towards where it was believed to live in Sprotbrough, but we are unable to confirm if it was reunited with its owner as it ran off from officers and we then could not locate it.
“No one came forward from our post on social media to say they were the owners.”
Meanwhile, an RSPCA spokesman said: “We've advised that we will come out to try to catch it if it is in an enclosed area it can't escape from, so it sounds like it's still at large at the moment.”
It was later spotted in Newlands Park, Sprotbrough and on the Trans Pennine Trail near Cusworth.