The Mid Yorkshire NHS Hospitals Trust, which runs the site as well as Pinderfields and Dewsbury hospitals, insist that Pontefract has a "vital" role to play in the future of the health service.
Last week, bosses confirmed that Pontefract's midwifery unit was to close until the first week of November because of staff sickness.
In July, the trust admitted staff were "nervous" about the future of the site after non-emergency surgery was cancelled on a number of days during the summer. But it insisted patients were not being diverted away from Pontefract.
Speaking at a Wakefield Overview and Scrutiny meeting on Monday, Coun Betty Rhodes said the closure of the midwifery unit was "disturbing".
She said: "We are concerned about the impact this is going to have, particularly on mums-to-be.
"We need reassurances that this is going to be short-term. The short notice that all of this happened with is very concerning.
"I find it very interesting that they've managed to say already when it will reopen again."
Senior officials from the trust have been invited to an urgent meeting of Wakefield's health scrutiny panel on October 11 to explain the move.
Coun Alan Garbutt said he'd been told of other treatments that had been taken away from Pontefract, with patients sent to Dewsbury and Pinderfields instead.
He said: "It's just another measure to try and run the hospital down to get it to the point where they can turn round and say, "It's isn't viable (to keep it open)".
But after the meeting, trust chief executive Martin Barkley, said: "I can confirm that there are absolutely no plans for the Trust to close Pontefract Hospital.
"On the contrary we are looking at ways we can further utilise the excellent facilities and skilled health professionals at the hospital, at the same time as reducing the need for local people to travel to Pinderfields Hospital.
"Pontefract Hospital has a vital role to play in the local NHS. We continue to serve the local population with the services we offer from there, which
include a 24-hour urgent treatment centre, planned surgery, day surgery, a number of outpatient clinics and inpatient rehabilitation for people who need round-the-clock care."