Has any of the "HN for ___" sites ever taken off and lasted?

You have to remember, HN is fully supported by YCombinator, and has a huge leg up on any possible similar sites. There will always be content thats encouraged to be posted here first from YC startups, and it will always be a valuable PR asset for those companies.

It doesn't have any pressures to make money, in fact it's basically a free place for PR and advertising jobs for portfolio companies

Generally, no, at least that I know of. Of the ones closely following the format, lobste.rs had a pretty good run, and designer news was busy enough to be worth visiting for a few years. With some more flexibility on format, product hunt might top the list.

HN is somewhat unique in its lastingness, and seems to have found a sweet spot in growth rate over the years that allows them to stave off the 3 things that will kill a website like this: silence, negativity, and grift. Most websites are so scared of the first one that they'll compromise on the second and third. Moderation is hard. Surely a large of dose of luck is also involved.