The Lady Victoria Colliery has housed the museum since 1984
The Scottish Mining Museum is facing a cash crisis following the loss of a third of its funding.
Both Midlothian Council and Historic Scotland have told the museum they are to stop their combined funds of about £156,000.
The museum, which is based at the former Lady Victoria Colliery in Newtongrange, Midlothian, is now in talks with the Scottish Government.
The colliery was voted Scotland's "Most treasured place" in 2007.
But it is said to need £2.5m to repair and restore its buildings.
Fergus Waters, director of the Scottish Mining Museum, said: "It is a very difficult time. [The cuts] represent a third of our revenue funding so we really need to have replacement funding in place by the end of March.
"But we are in very positive talks with the Scottish Government about finding alternative sources of funding.
"It has been a great year for Newtongrange - our Lady Victoria Colliery was voted Most Treasured Place by the public, we've had national museum accreditation and our visitor numbers have been good but our funding has been a serious problem for a while and this loss means the whole strategy has come unstuck."
Dr Jim Arnold, chairman of the Association of Independent Industrial Museums and Heritage Sites in Scotland and a director of the New Lanark Trust, said Scotland's other industrial museums were facing similar problems.
He added: "They are large scale sites - not particularly expensive in the first place but expensive in terms of upkeep. They tend to be large railways or mines and sites as big as that are going to need significant money and significant visitor numbers to keep themselves efficient."
"We have had 20 years of government reports and hand to mouth funding. Although we have national status and in New Lanark's case, world heritage status, the funding has not followed and that guarantees periodic crises - you can't get out of that and every major industrial site has that pattern."
Dr Arnold said it was important to look for potential solutions from other countries, using the example of England and Wales where the mining museums are centrally funded.
The Lady Victoria Colliery, named after the wife of the Marquess of Lothian, opened in the 1890s and became renowned as one of Scotland's first "super pits", with a workforce of almost 2,000 at its peak.
By the time it closed in 1981, the colliery had produced a record 40 million tons of coal, all hauled up the 500-metre shaft by the largest winding engine in Scotland.
The A-listed complex is now said to be one of the finest surviving examples of a Victorian colliery in Europe, and has been home to the extensive collections of the Scottish Mining Museum since 1984.