  Motivated by a class of flux compactifications of type IIA strings on rigid
Calabi-Yau manifolds, preserving N=2 local supersymmetry in four dimensions, we
derive a non-perturbative potential of all scalar fields from the exact
D-instanton corrected metric on the hypermultiplet moduli space. Applying this
potential to moduli stabilization, we find a discrete set of exact vacua for
axions. At these critical points, the stability problem is decoupled into two
subspaces spanned by the axions and the other fields (dilaton and Kahler
moduli), respectively. Whereas the stability of the axions is easily achieved,
numerical analysis shows instabilities in the second subspace.
