We analyze the effect of order-parameter fluctuations on the superfluid density wave states known as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases in neutral Fermi systems. We identify a tendency to renormalize the ordering wave-vector to zero by fluctuations. The results indicate that the FFLO states may be unstable as thermodynamic phases both in dimensionality d=2 and d=3 at temperatures T>0.