Ms Cooper has again attacked local health bosses who are proposing to shut the Friarwood Birth Centre at Pontefract Hospital before the end of the year, claiming that "dodgy figures" have been used to justify the move.
The Mid Yorkshire Hospitals NHS Trust, which runs the site, insists that no final decision has yet been made, but stands by its claim that the unit is underused and that midwifery staff would be best employed at Pinderfields Hospital.
The trust and Wakefield Clinical Commissioning Group (CCG) have presented the case for the closure to NHS England, who would need to give permission before the move goes any further.
But Ms Cooper, who confronted the trust about the plans before Christmas, is trying to arrange her own meeting with Simon Stevens, the NHS' chief executive, to lobby for the unit to be saved.
Describing the proposals as a "complete outrage", she said: "The trust seemed to be backing off their plans before Christmas, but now it’s clear they haven’t been listening at all.
"They have repeatedly used dodgy figures to try to close our services.
"Once again local health bosses are trying to solve problems at Pinderfields by closing good services at Pontefract - it is completely unfair.
"I’m sick and tired of them always hitting services in the towns and always moving them back into cities instead.
"This is bad for maternity care and family choice, goes against all national evidence, and is unfair on local mums.
"I’m urging the Trust board to reject this plan and calling for an urgent meeting with NHS England who should rule these cuts out now."
The trust has said it will listen to opinions from people who have used Friarwood or may use it in the future, but has strongly denied suggestions that the statistics they've used are untoward.
The CCG was due to start a public consultation on the issue before the end of January, though no details have yet been released about how people can take part in this.
Martin Barkley, the trust's chief executive, said: "As has been the case for some months now, it remains our intention to review the service we provide through our midwifery-led maternity unit at Pontefract Hospital.
"The facts speak for themselves: approximately 2,000 women from Pontefract and neighbouring areas give birth each year but only around 200 choose to have their baby at Pontefract’s Friarwood Birth Centre.
"Even before the temporary closures of the unit last year, the numbers of births were still low: in 2016 we had only three or four births per week, despite midwives at the unit making every attempt to promote the service to local
“Midwifery-led units like the Friarwood Birth Centre are staffed 24 hours a day, seven days a week.
"Given the low demand and the need to use NHS resources to best effect, it is
right and proper that we examine this issue.
"We have a responsibility to make sure we are making the best use of our midwifery staff across all our hospital sites to enhance safety and patient experience."