[MisterMuncher]

Have there ever been any cases of an anti-vaxer's child dying from the disease that a particular vaccination would have prevented?

I can't think of a specific example - but most high profile anti-vaxers are celebs "speaking their branes" - with excellent access to money-no-object treatment.

One lad in my primary school class died of complications from what started as a cold.
His parents were members of a Christian sect/cult which didn't believe in medical treatment.
There was a bit of a fuss when it transpired that he'd never visited a doctor, and their brethren were attempting a cure through the power of prayer.
9 years old, wonderful piano player.

IIRC, James Hetfield of Metallica fame, was raised in a Christian Scientist home, and his ma died refusing cancer treatment because of her faith. It happens surprisingly frequently, The J-Dubs policy on blood transfusions has claimed quite a few, too.