  We study the generation of magnetic fields during inflation making use of a
coupling of the inflaton and moduli fields to electromagnetism via the photon
kinetic term, and assuming that the coupling is an increasing function of time.
We demonstrate that the strong coupling problem of inflationary magnetogenesis
can be avoided by incorporating the destabilization of moduli fields after
inflation. The magnetic field always dominates over the electric one, and thus
the severe constraints on the latter from backreaction, which are the demanding
obstacles in the case of a decreasing coupling function, do not apply to the
current scenario. However, we show that this loophole to the strong coupling
problem comes at a price: the normalization of the amplitude of magnetic fields
is determined by this coupling term and is therefore suppressed by a large
factor after the moduli destabilization completes. From this we conclude that
there is no self-consistent and generic realization of primordial
magnetogenesis producing scale-invariant fields in the case of an increasing
kinetic coupling.
