Lesley Cameron, who is a co-owner of the cinema with her two brothers, told the BBC that the business was facing the “biggest financial challenge” in its history.
"We are really struggling and have had no grants. We need help,” she said.
Revealing that the family is spending more than £20,000 a month just to maintain the cinema at its Newbattle Terrace home, Mrs Cameron explained: “You can't imagine all the costs that are involved.
“When the old girl was shut down things were working but now we are finding little IT things that are going wrong and we are having to get them fixed.
"We have also had to soak the cinema in heat so it doesn't get damp.”
At the start of lockdown Mrs Cameron and her brothers removed 80 seats from its four screening rooms and ripped out the box office, but repeated attempts to get going again have been stymied.
Mrs Cameron said: "We thought we were going to be able to reopen in April, we had no idea it would be this long.
"We have kept trying to reopen but every time the distributors have pulled the films so we have had no product to show.
"We have been trying to keep the cinema alive so we are ready to do business as soon as we are able to.
"We keep thinking we will be able to reopen but then something comes along to stop us.
“It's the not knowing when we can reopen but having to be poised ready to go that is really hurting us."
In a bid to raise money, Dominion has begun selling off its prized collection of classic movie posters, including The Dirty Dozen, Vanishing Point and E.T. The Extra Terrestrial.
The Dominion, founded by Lesley’s grandfather, William Cameron, in 1938, is an art-deco architectural landmark in the Capital, and one of only two family-run cinemas in Scotland.
But Mrs Cameron warned that the coronavirus pandemic might spell the end of the business.
"We have come through World War Two, survived the opening of multiplexes - so we don't want to have met our match by Covid-19, but we just might have."