A few brands have earned that status for me. Quality and timeless design tend to be one reason. Another is that certain brands just "work" for me in a particular way.
St. John, for example, is expensive but I have never had a piece from them fail to make me happy. I'm still wearing some of their classic Milano knits 20 years later: pencil skirts and tank tops. Clean lines suit my curvy figure. But the cost... I pace myself with this brand. I must LOVE a piece to buy it. And then I wear--and love--my purchase to death.
I also love Lands End. They are my go-to brand for jeans because for whatever reason theirs fit me every time. I have high-waisted jeans of theirs from, yep, 20 years ago that are now back in rotation, faded but giving me great fit. Love my LE shirts, too. Good fabric and well made. LE cashmere sweaters have held up well over the years, as have their winter coats. Good quality at a good price... great if on sale. I will add LL Bean here, too. Quality basics.
Paul Green boots and shoes. Perfect fit every time. I know when I buy I will be wearing it straight out of the box.
Some other brands I always look at and will buy with trust are still a bit hit or miss. Eileen Fisher. Theory. Halogen. Burberry. Helmut Lang. But I wouldn't call them BILF, just favorites.