Arthur Streeton, one of the fathers of Australian impressionism, painstakingly captured the beauty of a rainy day over Sydney Habour in 1893.

Now that oil panorama canvas hangs on the first level of the National Gallery of Australia, where it faces the risk of being rained on itself.

As the Australian War Memorial gears up for a controversial half-billion dollar upgrade – which will add 10,000 square metres of exhibition space – other national cultural institutions in Canberra have been struggling with the basics.

Since the Coalition came to power in September 2013, institutions such as the National Gallery, the National Film and Sound Archive and the National Archives have been ordered to find more than $75m in savings – dubbed “efficiency dividends” in bureaucratic jargon.

Among the vital tasks threatened by the cuts is the preservation of Australia’s audio and visual archives through digitisation.

So dire have the National Gallery’s financial woes become that building maintenance has been neglected. Money earmarked for acquisitions has been raided for running costs, according to an auditor general report released in June.

Auditors found the gallery’s cash flow problems could endanger the $6bn art collection, while solvency was also a major risk. The audit said the backlog of building maintenance work had grown to $46.7m. So far the government has stumped up $21.5m over four years.

When it rains staff have been scrambling to place buckets under the leaks. The audit report said there had been 14 incidents of water leaks damaging art works on display and in storage.

“Weather events in February 2018 resulted in major water leaks that put over 30 works of art at risk of damage – one was directly affected with water damage and several showcases had water exposure,” the report said.

Without decisive action, we face the prospect of losing a substantial part of the memory of events that shaped Australia David Fricker, director-general, National Archives

“Consistent water leaks during heavy rain events also impact on the [gallery’s] overall environmental management, increase mould and insect activity and can place the public at risk.”

Among urgent items on the gallery’s to-do list are replacing a fire system at the end of its life; upgrading environmental control systems to ensure art is not damaged from temperature and humidity fluctuations; and fixing an ailing security system.

The storage warehouse in the Canberra suburb of Hume is 95% full. The audit report found in some cases artwork was not being stored properly at the gallery’s Parkes premise. Sometimes works were clogging up fire exits or gathering dust “on mobile racks for long periods”.

The gallery’s average staff head count is at 217, down from 250 three years ago, according to its latest annual report.

The gallery has been grappling with annual budget cuts to its operational running costs since 1987. The current funding level is $47m a year, the same amount as in 2007, former director Gerard Vaughan wrote in submission to a parliamentary inquiry this year.

Across the lake, the National Film and Sound Archive is in similar trouble.

There’s a race against time to digitise its collection of analog audio and video tapes. A submission to a parliamentary inquiry from Ray Edmondson, president of the archive’s friends volunteer group, said the preservation work was tracking at a third of the rate needed to meet a 2025 deadline.

“The [archive] is in a Catch-22 situation,” Edmondson wrote. “It cannot increase digitisation without further reducing other activities. It cannot restore its public profile without reducing preservation and acquisition work.”

Edmondson said potential sponsors would not be “attracted to an invisible institution”.

The archive’s staff fell from 215 in 2012-13 to 164 in 2016-17, according to its submission to a parliamentary inquiry.

It said its headquarters in Canberra is no longer fit for purpose and it hopes to secure government support for a new facility next door to the National Museum of Australia on the shores of Lake Burley Griffin.

Budget cuts had, for a period, resulted in reduced opening hours and the closure of the exhibition gallery, which has since been reopened, it says. The library is now open one day a week. Part of the headquarters and carpark have been leased to raise money.

Over at the National Archives, there’s another mammoth preservation task that urgently needs $25m.

The archives must digitise 190,000 individual audiovisual items on magnetic tape that will deteriorate within seven years. The collection includes classic TV shows such as Countdown and Playschool, as well as examples of ASIO surveillance, Antarctic exploration and Indigenous languages.

“Imagine losing forever all video footage of your children growing up,” director-general David Fricker said in a statement.

“Without decisive action now, the heartbreaking prospect of losing a substantial part of the memory and evidence of the events and decisions that shaped our nation could soon become a reality.”

Fricker had 429 staff in the 2013-14 financial year but that has now slipped to 355. Earlier this year the archive indicated a further 40 jobs were at risk in the next two years.

As the youngest and smallest of all the national cultural institutions in Canberra, the National Portrait Gallery is breathing slightly easier, according to outgoing director Angus Trumble.

Since he started in 2014, the gallery has lost four full-time jobs and now has 49 staff. Trumble lamented the gallery had to scupper two ambitious ideas for international exhibitions because it couldn’t afford to pursue them.

“I think we have reached the limit of our capacity to go on [absorbing cuts] without affecting our program delivery,” he told Guardian Australia.

Arguments that institutions should be tapping into corporate sector sponsorship or private donors to make up a shortfall of government funding, don’t impress Trumble.

“Enormous corporations like your banks, insurance companies and airlines get more for their sponsorship dollars in [cities] of 4-5 million than in communities of 400,000 people like in Canberra,” he said.