Constructing a building that would last 1000 years is not particularly hard with modern engineering and materials.
The hard part is, first and foremost, getting someone to pay for it. I'm not going to live 1000 years. My great grandkids likely won't even live to see the year 3022. Why would I spend orders of magnitude more for a house if a structure meant to last ~100 years serves my needs perfectly?
My friend just needed to redo the foundation on his house. He could have spent 10-100x what he needed to and installed a reinforced concrete foundation with deep steel pylons. But that would have been a waste of his money when wooden peirs works just as well for all his intents & purposes.
The second problem is making sure people want to maintain the structure for 1000 years, or at least not tear it down. I don't think this is as hard as the other comentors are saying, though. Just don't build the house in a city. The house will be torn down if it's in a city. The house has a good chance of staying a house if it's built out in the countryside on a decent plot of land. Nobody will ever want anything from that structure but to live in it, so it will be maintained.