About 20 babies have been born at an alternative hospital since a district maternity unit was temporarily closed, health bosses have said.
Royal Devon University Healthcare NHS Foundation Trust temporarily suspended births at North Devon District Hospital in Barnstaple on August 11 because of staffing issues.
The move has drawn heavy criticism from pregnant women who say they now face long journeys to give birth in Exeter, about 54 miles (87km) away. The county council leader said the closure was a "catastrophic failure of senior management".
Sam Higginson, the trust's chief executive, said he wanted the suspension to be short but could not commit to a reopening date.
Higginson said changes had been made to services in Exeter to help deal with extra patients from other parts of Devon and Cornwall who would normally go to North Devon District Hospital for births.
He said staff who normally worked in north Devon had been asked to continue supporting women and babies in Exeter while making sure there were enough beds and theatre space.
The trust needed to "be creative" with its recruitment strategy to promote north Devon as a great place to live and help fill vacancies, the health boss said.
He said his number one priority was to keep the temporary suspension as short as possible, but he could not say when it would be lifted.
"We haven't committed to a specific date yet," he told BBC Radio Devon.
"We're trying to get it reopened as quickly as we can.
"It is totally dependent on us being able to attract both permanent and temporary staff."
On Saturday, hundreds of people protested in Barnstaple over the closure.
Rebekah Hester, from Ilfracombe, is classed as high-risk because she has pre-eclampsia, a complex condition that causes high blood pressure and can put both baby and mother at risk. She said she was looking at tutorials on giving birth and home deliveries.
Hester said coming to the realisation that a birth may not go as planned was "terrifying".
She said: "You turn to midwives and you turn to Google, and Google is saying an hour-and-a-half drive is too far, you need to find a closer maternity unit, or you need to watch these tutorials on giving birth and home deliveries."
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Twenty Babies Born Since Maternity Unit Closure