We report on systematic and high-precision measurements of the evolution of electron beams in a laser-wakefield accelerator (LWFA). Utilizing shock-front injection, a technique providing stable, tunable and high-quality electron bunches, acceleration and deceleration of few-MeV quasimonoenergetic beams were measured with cutting-edge technology sub-5-fs and 8-fs laser pulses. We explain the observations with dephasing, an effect that fundamentally limits the performance of LWFAs. Typical density dependent electron energy evolution with 57–300 μm dephasing length and 6–20 MeV peak energy was observed and is well described by a parabolic fit. This is a promising electron source for time-resolved few-fs electron diffraction.