The campaign to save maternity and children's services at the Friarage Hospital in Northallerton has been stepped up after new research.
The results from a survey of 19 other small hospitals, similar to the Friarage, show the majority are confident in sustaining services in their local areas.
The NHS plans to transfer the maternity unit services and overnight paediatric care to James Cook University Hospital in Middlesbrough. Part of the reason, it says, is because of a lack of doctors.
But campaigners now say the survey reinforces their claim that there's no need for that to happen.