Folklore conjecture on nonvanishing of quadratic twists

Let $E$ be any elliptic curve over ${\mathbb Q}$, let $r$ be a positive integer, and let $E^{(M)}$ denote the quadratic twist of $E$ by $M$. A square-free integer has exactly $r$ prime factors when it is the product of exactly $r$ distinct primes. Folklore nonvanishing conjecture. For any elliptic curve $E$ over ${\mathbb Q}$ and any positive integer $r$, there are infinitely many square-free integers $M$ having exactly $r$ prime factors such that

$$L(E^{(M)},1)\neq 0.$$

This is a nonvanishing prediction for quadratic twists with prescribed numbers of prime factors; the source calls it folklore and does not state that it has been proved or disproved.