Is there a secret to the latters' success? Or is it just a combination of luck and finely tuned business sense?
There is no secret. Different eras and types of markets are overlapping in your post, with very different conditions that should be judged individually.
Zac Posen peaked with his debut in 2001. It really does not get better for him than in those first years when he had the biggest models in his show and was featured routinely in mainstream media, huge shows like SATC and all over the pages of Vogue every single month. He was Anna Wintour's 'golden boy'. Proenza Schouler were close behind. Like most designers/models/anything Anna Wintour overhypes, they benefitted from her 'absolutism' in fashion and the monopoly of Vogue. Social media is a new form of media but media was no less aggressive then, just more authoritarian because even if you scratched your head wondering why something clearly subpar was being pushed down your throat, you thought you were alone. I think many consumers who supported these labels because they were Vogue-approved would not have been able to give a compelling, detailed answer at the time on
why they were great and deserving of sky-rocketing success.
Christopher Kane was essentially the same but in London and for the late 00s.
What all of these 3 have in common (which gained them a lot of criticism at the time), is that they were extremely limited, borderline fraudulent designers. They were skirts and dresses labels that anchored their entire success on simply changing the theme/color/texture of the same pieces. Kane was the worst at it and also the best example. From his debut in the summer of 2006, he comfortably relied on the hype, presenting essentially the same collection and it's not until 8 years (!!) later, for fall of 2014, when he creates a more cohesive collection but by the time, it was too little too late, and attention had already waned.
When you're this limited and rely on costume-y themes that embody popular trends that speak to the youth of the time, you inevitably confine yourself to generational appeal and generations always repel what the previous generation worshipped so that's their death sentence.
Off-White and Vetements were founded over a decade later in 2014, as social media and influencers are on the rise. We're only a decade after their foundation and just like Posen and Kane in 2014, they're already irrelevant (Vetements) or on their way with no return (OW), and probably scrambling, but it's too late for them to break out of the cage they built for themselves.. even if they did try to present more than just streetwear and suddenly came up with, say, a collection of perfectly tailored trousers or timeless shirts (lol), they represent a generation of tumblr and whatnot, things will just never be as good as they were for them in 2015 no matter who is the genius behind their social media because each generation is composed by different information, vocabulary and ambitions and most of all, a need to distinguish themselves from the previous one and social media (or any form of media) is not stronger than that.
.. and RO is everything but a young label. Same wave that brought Miguel Adrover and reliant on the same market that consumed Carol Christian Poell. More niche/word-of-mouth with still no need of Vogue nor SM. RO is kind of a joke now but he was not a one-trick pony or presenting the same sweatshirt or skirt with different colors, and he built a solid business, that's why he endures and why despite his ridiculousness and horniness taking the wheel of his shows these days, his label will most likely outlive Off-White.