As zegh said, there was initially no reason for the BoS to crush the NCR. By the time their interests came into conflict with each other, the NCR had a population of hundreds of thousands, which means probably tens of thousands of troops. The Brotherhood were probably closer to a few hundred to a few thousand members, due to not letting wastelanders join in any great numbers, and relying on antique power armour, which is unlikely to be in great supply. Their aim was never expansionism or increasing their numbers, it was to hoard technology.
It's hard to bring down a soldier in power armour, but by no means impossible. High-calibre armour piercing round to the head. EMP. Flamethrower to cook whatever is inside. Direct hit from an artillery shell. A power-armoured soldier is going to kill a lot of troopers before their number comes up and they get stopped by something like that, but they are not immortal. The NCR can afford many times more losses than the Brotherhood, and eventually the Brotherhood are going to be dead or driven out of the NCR, long before the NCR run out of troopers to throw at them. So the Brotherhood didn't disappear from NCR territory for no reason, they disappeared because they had all been shot.
It's hard to bring down a soldier in power armour, but by no means impossible. High-calibre armour piercing round to the head. EMP. Flamethrower to cook whatever is inside. Direct hit from an artillery shell. A power-armoured soldier is going to kill a lot of troopers before their number comes up and they get stopped by something like that, but they are not immortal. The NCR can afford many times more losses than the Brotherhood, and eventually the Brotherhood are going to be dead or driven out of the NCR, long before the NCR run out of troopers to throw at them. So the Brotherhood didn't disappear from NCR territory for no reason, they disappeared because they had all been shot.