Danny Sage said his son Jamie (19), who was a glazier, had been unable to work since he suffered two compound fractures at the park in September 2015.
"I still think there was something underneath [the trampoline] that he hit hard."
Jamie underwent a six-hour operation but the injury did not meet WorkSafe’s investigation threshold, Mr Sage said.
"I didn’t at the time, but I actually now would like to see it shut down and dare I say it, someone’s going to get killed there, I think."
The comments follow a series of horror stories of people being injured at the park, including an incident on Wednesday, when a woman in her 20s was flown by helicopter to Christchurch Hospital after sustaining spinal injuries in a fall there.
Jessica Stumbles (10), of Dunedin, had undergone one operation and faced the prospect of two more after suffering a compound ankle injury at the park in October.
"The force of the tramp coming up while she was coming down left her ankle hanging off."
She believed the environment at the park was not adequately controlled.
"I’m no wrap-your-kids-in-cotton-wool parent. We have always had a trampoline in the backyard but I don’t think the Leap environment is properly controlled."
Jessica was still limping and would undergo two more operations in the next year to remove wires from her ankle.
An orthopaedic surgeon had advised she would require orthopaedic treatment until she was 16 because her growth plate had been "smashed".
Further investigation into the safety of trampoline parks was needed, Mrs Stumbles said.
"I would like there to be an audit at the A&E department of accidents from Leap.
"You can’t argue with that."
A Leap spokesman said he did not know how many ankle injuries had occurred at the park since it opened in November 2014. However "all practical steps" were taken to ensure the park was safe.
"Any injury that we become aware of is considered important.
"The definition of serious is open to some interpretation but we notify all notifiable injuries to WorkSafe as per their definition and requirement."
Karen Peacock, of Dunedin said her daughter Emily (14) was still traumatised after also suffering a compound ankle fracture at the park in January.
"Luckily for her, there was already an ambulance there, because a boy broke his leg in the same session."
Emily’s ankle bone pierced her skin.
She had missed the first two weeks of high school and was still undergoing physiotherapy.
An email to the managers of the park suggesting ways to improve a safety briefing her daughter was given before playing at the park was ignored, Mrs Peacock said.
She believed a lack of staff control at the park contributed to the accident.
"In places like that, how can you control it when there are people jumping around everywhere.
"You might have a 120kg man jumping beside a small child.
"If I’d have known the risks I never would have sent her there."
The Leap spokesman said one session, limited to 60 people, ran at the park at a time.
A minimum of one staff member monitored 20 participants at a time and staff went through rigorous training.
"We provide a full safety briefing before every session and staff are trained to monitor and intervene where risky behaviour is observed.
"At the end of the day we cannot control people’s decisions 100%"
A WorkSafe spokesman said 28 incidents had been reported to the department by the public and Leap management since the start of last year, but 27 were below the investigation threshold.
WorkSafe was investigating Wednesday’s accident, the spokesman confirmed.
