"We are in a precarious financial position, and our board has said if we don't get the funding we will move to wind down, to be effective in June, which is an absolute tragedy."
The group had never sought government funding before, rather relying on member fees, she said.
Their pitch to the Government was that the group was unique and filled a gap through its ability to co-ordinate the various rural sectors to identify the potential issues affecting rural health and find solutions.
That information was then given to the Government to help with policy decision-making as it related to rural people's health and wellbeing.
Ms Thompson said she and RHAANZ chairman Martin London were due to meet Mr O'Connor on Thursday in a last ditch effort to gain support to continue being a health voice for New Zealand's communities.
"One in every five dollars generated in the economy either directly, or indirectly,
comes from the agri-food sector.
"Yet it does not feel like we get anywhere near this level of resourcing or attention.
"The endless gnawing away at services for rural communities has to stop. Rural Kiwis have lost their hospitals and schools. We are facing underfunded health services, emergency services, midwives and airports.
"For this organisation to disappear from the scene, at a time when rural health itself is as precarious as ever, would be a terrible loss of goodwill, synergy and expertise."
She said they were asking the Government to contribute about $600,000 - $1 for every person identified as rural in the country.
"We are being reasonable - our individual members will work to plug the gaps.
"It seems inconceivable that a Government that has campaigned so hard on improving the lot of rural New Zealand would not support us."
Ms Thompson said there were only two other national rural health alliances in the world - one in Australia and one in the United States, and both received central government funding.
"New Zealand needs to follow that lead."
Federated Farmers was a member organisation of the alliance and national president Katie Milne, who was also a RHAANZ executive, said gaps in health services in rural New Zealand were becoming more and more apparent.
"If the alliance is starved of funding and is forced to close, those gaps and shortfalls could snowball, leaving the health and wellbeing of rural residents at significant risk."