Sharron and Edward Parker, who run Yellison Goats' Cheese in Bradley, between Keighley and Skipton, say that because restaurants and pubs have closed virtually all their business has disappeared - and is appealing for farm shops to give their product a try.
The farmers, who met aged 16 and have three children, trade to wholesalers and their Great Yorkshire Show award-winning cheese has been used by restaurants such as Le Caveau in Skipton and Pipe and Glass in Beverley.
Mrs Parker, 48, said: "This is a real worry for us. I might not have a job after this."
The family, which runs from Sire Bank Farm, sell 150g and 800g soft cheese logs, crowdie based on a Scottish recipe, milk and curd, most of which is traded to wholesalers.
As winter winds up and the goats are "in kid", the coming months are usually prosperous, but with restaurants forced to close while Covid-19 continues to spread, the family is seeing little return on the costly process of milking a 70-strong herd.
Mrs Parker said: "We pasteurize every five days and use about 75 kilos of cheese. Now, really, we should be doing that every three days with the amount of milk we've got. Obviously we can't."
Mrs Parker said: "It's just nothing now."
She added: "The sales up go and they stay high through summer.
"Obviously they've not even gone up, they've gone down."
"We're trying to stay positive and hope we can [get] through this."
To get them through this insecure period, Mrs Parker said that they are able to deliver 20 to 30 logs to farm shops or courier their products.
She added that the business just last month won Safe and Local Supplier Approval (SALSA) recognition, and hopes supermarkets such as Morrisons - which has traded with such regional firms - will take note.
It was originally owned by Steve Akrigg at Yellison Farm, who died after a cancer battle on Christmas Day in 2013, and the herd was moved to the Parkers' in February 2014.
"Unfortunately he was never well enough to come and see where his goats were moving," said Mrs Parker.
The couple's children, university student Georgia, 19, Joseph, 17, and Archie, 11, also help out on the farm when they can.
To learn more about the company and see its produce, visit: https://www.yellisons.co.uk