The birth unit at Pontefract Hospital will close for six weeks due to a staff shortage.
Mid Yorkshire NHS Hospitals Trust said staff sickness was the reason the Friarwood Centre had been closed on several occasions over the past month.
Speaking at a meeting of Wakefield's health scrutiny committee on Thursday, chair Coun Betty Rhodes said: "There's lot of factors that can be taken into account. One of them has got to be the safety of patients and staff, but there must be other factors as well.
"Other than that we've had no information. We need a lot more details than what we've been given today."
Senior officials from the trust will be asked to attend an emergency health scrutiny meeting on October 11, to explain the reasons behind the closure.
Last month the Mid Yorkshire Hospitals NHS Trust said the centre would not be permanently closed after the birth facility shut its doors without warning.
But earlier this week a staff member, who did not want to be named, told the Express the centre had only been open "on eight to 10" occasions over the previous six weeks.
They said the closures were not announced to patients and midwives with prior warning, and staff were often unclear where they would be working.
They said: "It is being made unsafe for women. Someone could end up giving birth in a car park if they turn up and the centre is closed.
"Women are forced to go to Pinderfields Hospital or even Dewsbury at short notice.
"It is not acceptable to remove that choice for patients."
Yvonne Rowlan, Assistant Director of Nursing and Midwifery, at the Mid
Yorkshire Hospitals NHS Trust said: “Our priority is to provide women with a safe and positive birthing experience, and we offer the full range of birthing options to local women – from home births and maternity- led units to consultant-led hospital births – across our three hospital sites at Pontefract, Pinderfields and Dewsbury.
"However, as has previously been reported, we have unfortunately had to close the Friarwood Birth Centre at Pontefract on a number of occasions in the last month due to a shortage of midwives, causing difficulties in maintaining appropriate staffing in all three birthing centres.
“We recognise this causes uncertainty for both staff and women who have chosen to birth at Pontefract. We have therefore regrettably had to take the decision to temporarily close the Friarwood Birth Centre for a period of six weeks to allow us to consolidate staffing.
“All women booked in to attend the midwifery-led unit at Pontefract have been informed, as have the staff at the unit, and anyone affected is encouraged to speak to their community midwife about their choices, which include birth centres at Pinderfields and Dewsbury.”