Pontefract Hospital's maternity unit could shut as early as October this year, if local NHS bosses are given permission for the move.
The Mid Yorkshire Hospitals NHS Trust, which runs the site, said they were seeking to close the Friarwood Birth Centre at the hospital last year, because not enough mums were using it to justify keeping it running.
Fewer than 200 women a year are having their babies at the unit, compared to around 6,000 at Pinderfields Hospital in Wakefield.
But the idea has attracted strong criticism from Pontefract and Castleford MP Yvette Cooper and local councillors.
Now papers detailing the proposed 'case for change', which have been handed to NHS England, say that if the decision is approved at national level, the closure could take place between October and December this year.
But despite the birth centre currently running as normal, documents suggest that it could still be subject to temporary shutdowns in the coming months.
This happened last autumn when a staff shortage resulted in the trust closing the unit for six weeks, with all bookings during that period moved to Pinderfields.
The papers, which will be discussed at Wakefield Clinical Commissioning Group's (CCG) board meeting next Tuesday, say the service, "Remains fragile from a sustainability point of view, leaving Pontefract MLU vulnerable to closure at short notice due to an inability to provide suitably qualified staff.
"The intention is to have a new service model in place by the end of 2019."
It is added: "The trust will be required to provide assurance that there is sufficient bed capacity on the midwife led unit at Pinderfields to
accommodate the small number of births that currently take place at Pontefract."
The papers also claim that the cost of a birth taking place at Pontefract Hospital is more expensive than the cost of one at Pinderfields.
The document says: "A low risk midwife led birth in Pinderfields MLU costs £2,932.
"In comparison, the same birth at Pontefract MLU costs £3,766. This equates to an additional £175,974 per year.
"Wakefield CCG has a duty to ensure best use of public funding in the context of significant financial challenge."
In a statement, Wakefield CCG said: "The governing body is not making a decision about whether to support any change at this time.
"They will be considering whether there is evidence that the way services are delivered should be reviewed.
"If the governing body agrees a review is necessary, they will set off a process which will involve going out to the public to seek views on possible solutions as well as getting independent clinical advice.
"The CCG will oversee this process and will be very keen to talk to people who have recently used maternity services or are likely to use these services in the future."
Local Democracy Reporting Service