It goes like this: My story includes a named manor house. Holcomb House, to be exact. I know what to do with the name when presented as a whole, but I am left to wonder if the word house, by itself, once established as referring to Holcomb House, remains majuscule? "I've been living and working in Holcomb House for over a year. The house needs quite a bit of work." or... "I've been living and working in Holcomb House for over a year. The House needs quite a bit of work."
I would say no. Here: https://www.bbc.co.uk/news/uk-england-berkshire-46348857 The BBC uses "cottage" in the second sentence after referencing the name of the building, Frogmore Cottage in the first sentence. Sometimes, you'll see "the Palace" when referring to Buckingham Palace, but that is actually a reference to the monarchy rather than the building.
Excellent. Thank you. Wasn't sure if this would be different US compared to UK since - while we certainly do have named houses and grand estates - they don't answer to any ties with nobility or peerage, so I wasn't sure if that would make a difference. ETA: We do a similar thing with "the White House" in the way it gets used to refer to the presidency, not the actual structure.