The only way this movement is going to die is when a sufficient number of parents watch their non-vaccinated children die or become horribly disfigured from long-since dealt with diseases.
Let's see. Four people have been hospitalized with measles in NYC this year. So far.
NYC has 8.3 million people.
So, three months worth of normal deaths translates to 20-odd thousand deaths in the City so far this year.
Assuming all four of the hospitalized measles victims die, that'll increase the death rate by 0.02% in NYC.
This is not the pandemic you're looking for to produce the effect you're hoping for (lots of anti-vax kids dying so as to convince their parents to give up their evil ways).
The REAL reason why the anti-vax movement is surviving is that it really doesn't matter much if you're pro-vaccination or anti-, so long as most everyone else is pro-. Until the anti-vaxxers become a significant fraction of the population (say, 10%), the side effects of being anti-vax won't be severe enough to be noticed on a societal level.