We report the observation of an unpredictable behavior of a simple, two-path, electron interferometer. Utilizing an electronic analog of the well-known optical Mach-Zehnder interferometer, with current carrying edge channels in the quantum Hall effect regime, we measured high contrast Aharonov-Bohm (AB) oscillations. Surprisingly, the amplitude of the oscillations varied with energy in a lobe fashion, namely, with distinct maxima and zeros (namely, no AB oscillations) in between. Moreover, the phase of the AB oscillations was constant throughout each lobe period but slipped abruptly by pi at each zero. The periodicity of the lobes defines a new energy scale, which may be a general characteristic of quantum coherence of interfering electrons.