For which manifolds or varieties is quantum cohomology known to converge? Are there any manifolds for which quantum cohomology is known to not converge? I seem to have the impression that quantum cohomology is known to converge for Fano manifolds or maybe toric Fano manifolds, but I don't know if this is actually true.

By "convergence" I mean convergence of, e.g., the genus 0 Gromov-Witten potential.