Double-beta decays of $^{100}$Mo from the 6.0195-year exposure of a 6.914 kg
high-purity sample were recorded by the NEMO-3 experiment that searched for
neutrinoless double-beta decays. These ultra-rare transitions to $^{100}$Ru
have a half-life of approximately $7\times10^{18}$ years, and have been used to
conduct the first ever search for periodic variations of this decay mode. The
Lomb-Scargle periodogram technique, and its error-weighted extension, were
employed to look for periodic modulations of the half-life. Monte Carlo
modeling was used to study the modulation sensitivity of the data over a broad
range of amplitudes and frequencies. Data show no evidence of modulations with
amplitude greater than 2.5% in the frequency range of $0.33225\,{\rm y^{-1}}$
to $365.25\,{\rm y^{-1}}$.