I don't think it's luck, mate.
I think it's perception. They think they're a big club, and they moan when they're not included in the list and they constantly act like you'd expect a big club that's down on its luck to act. Hence they're perceived as a big club.
United and Liverpool have been big since the 60's. United have been England's team since Munich. And Shankly really did do a damn fine job branding the filth. Following Shankly with winning everything in sight just solidified the work he did.
No brand is unassailable of course. Precisely why massive Everton of the 1980's are now plucky little Everton of the 2010's. United will have a long, long way to fall though, and they have enough money to stop the descent, but that may still not be enough. Liverpool have already lost a huge amount of their brand power. No one except mutants believes they belong in the discussion with Barca, Bayern, Real, and United. They definitely would have 20 years ago though.
I personally believe Chelsea and City are setting themselves up for long term success. It takes time to build a brand. It takes time to burn yourself into the public's mind. They will do it if the money keeps flowing, then the brand will keep them there. If the money spigot is shut off too soon, they may well fall away as (Chelsea) is building almost exclusively through success on the pitch. City are a more interesting outfit though. They're expanding across the globe, with NYCFC and Melbourne(?). They keep ticket prices low to keep fans happy, and they are really working the commercial aspect of their club.
City, I think, are the first English club that are devoting just as many resources to 'Manchester City' as they are to MCFC. They see it as a business and are treating it as such. Their success will depend on time as well, but I suspect it will be a very long lasting success if they pull it off...like the New York Yankees or LA Lakers. It's more about the logo than the team.
Arsenal keep on keeping on. I think a lot of their brand is built on Wenger and CL. When he goes, or/when they stop being automatic CL qualifiers it will be interesting to see the fallout.