  We consider the non-perturbative superpotential for a class of
four-dimensional $\mathcal N=1$ vacua obtained from M-theory on seven-manifolds
with holonomy $G_2$. The class of $G_2$-holonomy manifolds we consider are
so-called twisted connected sum (TCS) constructions, which have the topology of
a K3-fibration over $S^3$. We show that the non-perturbative superpotential of
M-theory on a class of TCS geometries receives infinitely many inequivalent
M2-instanton contributions from infinitely many three-spheres, which we
conjecture are supersymmetric (and thus associative) cycles. The rationale for
our construction is provided by the duality chain of arXiv:1708.07215, which
relates M-theory on TCS $G_2$-manifolds to $E_8\times E_8$ heterotic
backgrounds on the Schoen Calabi-Yau threefold, as well as to F-theory on a
K3-fibered Calabi-Yau fourfold. The latter are known to have an infinite number
of instanton corrections to the superpotential and it is these contributions
that we trace through the duality chain back to the $G_2$-compactification.
