It wouldn’t necessarily die out even in that case, because there are lots of other factors than that predator involved in who survives and reproduces. There are going to be brown haired people who die for other reasons, and blonde haired people who aren’t killed by the predator.

Even if the recessive gene is always fatal if you get two copies of it, and the gene is the only factor in survival, it’s still going to take a long time for it to disappear, because humans take so long to get to reproductive age.