I can definitely reason that given how massive these buildings are, that they're probably repurposed for non-residential use now. Are there families who still can afford to upkeep them? How much funding is dedicated to historical preservation?
That really depends on the house and family in question. Some, like Chatsworth, are still owned and lived in by their families. Some, like Bristol's Dower House, were redeveloped as multiple residences (Bristol's Dower House previously served as a military hospital and psychological unit). Some, like Bristol's Bishop's Palace or Bath's Prior Park are now schools. A great number have been placed under the auspices of The National Trust, founded in 1895 as The National Trust for Places of Historic Interest or Natural Beauty.
A wide practice when they became difficult to maintain in the early half of the 20th century was to donate them to the NHS or psychiatric charities to be run as hospitals. A great many delapadated old manor houses have connotations similar to lunetic asylums in British culture which is a little sad. Most counties in England have major NHS hospitals or offices still running out of manor houses. Until recently historical protection rules and building regulations have made the older and more delapadated buildings unappealing to the private sector for residential development. The simple reason for a lot of their ruin is that we have so many of them. The National Trust cannot hope to maintain all of the hundreds of manors up and down the country as well as the various castles, museums etc.
However, in the last decade or so there has been a realisation that these buildings are no longer as viable hospital sites, there have been changes in building regulations and the large landholding has become attractive for private development companies. So agreements are being struck where companies build new hospitals on a much smaller plot of land in return for the current NHS old manor house land. The grounds of the manor house gets broken up into housing plots and turned into suburbia and the grand central manor house is usually transformed into high status flats.
Here's one example in Kent
Three more old hospital manor houses in Kent are due to go the same way in the next 10 years. It's sort of a win for the population and NHS to get new modern hospitals but companies are making a massive profit out of these deals and you can't help but think more funding for the NHS could have been wrung out of the deals. It is good thing overall for the buildings themselves as they will now be maintained and enjoyed by a number of residents for generations.