  We present a comprehensive investigation of the evolution of helimagnetic
correlations in Mn$_{1-x}$Fe$_x$Si with increasing doping. By combining
polarised neutron scattering and high resolution Neutron Spin Echo spectroscopy
we investigate three samples with $x$=0.09, 0.11 and 0.14, i.e. with
compositions on both sides of the concentration $x^* \sim 0.11$ where the
helimagnetic Bragg peaks disappear and between $x^*$ and the quantum critical
concentration $x_C \sim 0.17$, where $T_C$ vanishes. We find that the abrupt
disappearance of the long range helical periodicity at $x^*$, does not affect
the precursor fluctuating correlations. These build up with decreasing
temperature in a similar way as for the parent compound MnSi. Also the dynamics
bears strong similarities to MnSi. The analysis of our results indicates that
frustration, possibly due to achiral RKKY interactions, increases with
increasing Fe doping. We argue that this effect explains both the expansion of
the precursor phase with increasing $x$ and the abrupt disappearance of long
range helimagnetic periodicity at $x^*$.
