One topical question in today's particle physics and astrophysics concerns the search for low-energy rare events. Spurious counts, resulting from environmental radiation, in particular neutrons, can easily overcome the signals of interest in this kind of research. Hence a quantitative evaluation of the neutron background and a full understanding of the parameters, which conditionate its intensity and energy spectrum, is particularly important. In this letter we will show and discuss the evidence of long-term fluctuations (in months scale) appearing in the measurements of fast neutron rate. The data were collected in the Baradello underground laboratory (Como, Northern Italy, 300 m.w.e. depth) from May 2002 until December 2003. We find a strong correlation between fast neutron rate and rain precipitation at the surface, but only when we introduce a phase delay of about one month between the timing of the rain flux and that of the neutron rate. We suggest that the fast neutron flux intensity is related to the moisture contained in the ground, which surrounds the laboratory walls, and we assume that the moisture depends on the rain quantity at the surface. The delay we find is consistent with the percolation time of the water from the surface to the underground laboratory. This mechanism should be taken into account as a possible systematic effect in any experiment which uses the signal rate modulation as a signature for a new physical phenomenon.