Trustees at Paxton House, on the banks of the River Tweed, say they need to raise the sum by June 20 to survive.
Ian Marrian, chairman of Trustees, said: “We want to reopen as soon as it’s safe for all and we’ll have to invest to ensure that safety.
“We cannot compromise on the conservation of our nationally significant collections and the glorious natural landscape.
“But every day without income makes survival a greater challenge.”
The venue closed its doors in March to help fight the spread of coronavirus.
The charity is almost entirely dependent for survival on visitor attendance and donations – around 90% of our revenue comes from paying visitors.
Ian said: “We would be so grateful for any gift you might make towards that target. Paxton House needs to raise funds for this covid-19 campaign and for other charitable purposes.
“The trust is also working extremely hard on a wider fundraising strategy to secure grant aid to cover the essential running costs for 2020.
“We hope that if and when we reopen, we can with your help and attendance, make these strange times a little happier.”
You can donate online at https://paxtonhouse.co.uk/supportpaxton/ or by mobile phone - to donate £5, text PAX100 to 70970 or to donate £10, text PAX100 to 70191.
It is also running a buy now, visit later scheme, making all house admission tickets valid until the end of 2021.