A young South Australian couple locked out of the state because of NSW's COVID-19 lockdown say they feel let down by the border exemption process.

Ben and Chelsea McQueen have been living in limbo just across the border in New South Wales.

It has been five weeks since they applied to SA Health for a border exemption. They are one of thousands of border exemption applications still being sorted out.

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"We've been stuck on a family friend's station an hour and a half away from Broken Hill," Ms McQueen said.

"It just feels like we haven't been cared about and it just feels like a massive guessing game," Mr McQueen added.

After a stint working in New South Wales the registered nurse and teacher are returning to start new jobs. Mr McQueen is fully vaccinated, while Ms McQueen has had her first dose.

"We had to be back in South Australia today to get our start dates and now we've missed it so we'll have to postpone our start dates for work," Ms McQueen said.

They are among 6000 travel exemptions currently being processed.

SA Health says it is working hard to respond quickly and compassionately to the high volume of requests and measures have been put in place to address delays.

The state opposition today called for more to be done.

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"It is clear that SA Health haven't been given the resources they need, in order to be able to deal with the long list of applications for people to return back to South Australia," Opposition Leader Peter Malinauskas said.

Mr McQueen labelled the delay unjust.

"It's a shame and it really, it hurts us a lot, and it's yeah, it's really unjust I feel," he said.

"We just hope SA Health can really step up their game."