Phase-sensitive optical time-domain reflectometry (φOTDR) is a simple and effective tool allowing the distributed monitoring of vibrations along single-mode fibers. We show in this Letter that modulation instability (MI) can induce a position-dependent signal fading in long-range φOTDR over conventional optical fibers. This fading leads to a complete masking of the interference signal recorded at certain positions and therefore to a sensitivity loss at these positions. We illustrate this effect both theoretically and experimentally. While this effect is detrimental in the context of distributed vibration analysis using φOTDR, we also believe that the technique provides a clear and insightful way to evidence the Fermi-Pasta-Ulam recurrence associated with the MI process.