  Motivated by recent experimental detection of Neel-type ($(\pi,\pi)$)
magnetic fluctuations in some iron pnictides, we study the impact of competing
$(\pi,\pi)$ and $(\pi,0)$ spin fluctuations on the superconductivity of these
materials. We show that, counter-intuitively, even short-range, weak Neel
fluctuations strongly suppress the $s^{+-}$ state, with the main effect arising
from a repulsive contribution to the $s^{+-}$ pairing interaction, complemented
by low frequency inelastic scattering. Further increasing the strength of the
Neel fluctuations leads to a low-$T_{c}$ d-wave state, with a possible
intermediate $s+id$ phase. The results suggest that the absence of
superconductivity in a series of hole-doped pnictides is due to the combination
of short-range Neel fluctuations and pair-breaking impurity scattering, and
also that $T_{c}$ of optimally doped pnictides could be further increased if
residual $(\pi,\pi)$ fluctuations were reduced.
