Air New Zealand said its priority was to try to get passengers home within the timeframe and restrictions set by the Government.
Brown said he was frustrated at not being able to get back to Gisborne under these circumstances.
"If there was any Covid crisis in the region [Tairawhiti], then I would want to be there.
"Fortunately that's not likely to be the case in the next few days but we don't know what's going to happen over the course of the next week."
Brown said New Zealand had taken the right approach in locking down but essential workers still needed to be able to get home.
"I think it's the right approach but essential workers still need to be able to get to where they are working.
"I don't think that we're the only two doctors that are stranded."
Brown and Roberts are booked to fly home to Gisborne tomorrow.
While they were initially concerned about tomorrow's flight not going ahead,
Brown said those concerns were subsiding with news of the case numbers.
It came after two of their flights, booked for Friday, were quickly cancelled. They went to the airport at 6am on Friday for their third flight booking to find it cancelled, while a fourth booking for Saturday was also cancelled.
Air New Zealand said it put extra flights on to get people out of Queenstown and while many were booked out, there were plenty of spare seats on the final flights to Wellington and Auckland.
An Air New Zealand spokesman said following the Government's announcement of a national alert level 4 lockdown, they operated their full domestic and regional schedule for 48 hours to allow people to get home, adding additional capacity where possible.
The Government extended the initial 48-hour grace period by 24 hours to allow Air New Zealand to fly more Kiwis home from Queenstown as that was where the most demand was coming from.
This exemption applied to flights from Queenstown only and did not allow them to operate a full schedule to all ports, the spokesman said.
"More than 6200 people heeded the Government's call and got on one of our flights out of Queenstown over the 72-hour period."
Once the Government announced the whole country would remain at alert level 4, they adjusted their schedule accordingly.
Air New Zealand was running a reduced schedule over the next few days to ensure essential workers and cargo could still move around the country. This did not include flights in or out of Queenstown.
"We'll then reassess our schedule in line with any further Government decisions."