The analysis of the early star formation history (SFH) of nearby galaxies, obtained from their resolved stellar populations, is relevant as a test for cosmological models. However, the early time resolution of observationally derived SFHs is limited by several factors. Thus, direct comparison of observationally derived SFHs with those derived from theoretical models of galaxy formation is potentially biased. Here we investigate and quantify this effect. For this purpose, we analyze the duration of the early star formation activity in a sample of four Local Group dwarf galaxies and test whether they are consistent with being true fossils of the pre-reionization era; i.e., if the quenching of their star formation occurred before cosmic reionization by UV photons was completed. Two classical dSph (Cetus and Tucana) and two dTrans (LGS-3 and Phoenix) isolated galaxies with total stellar masses between 1.3× {10}6 and 7.2× {10}6 {M}ȯ have been studied. Accounting for time resolution effects, the SFHs peak as much as 1.25 Gyr earlier than the optimal solutions. Thus, this effect is important for a proper comparison of model and observed SFHs. It is also shown that none of the analyzed galaxies can be considered a true fossil of the pre-reionization era, although it is possible that the outer regions of Cetus and Tucana are consistent with quenching by reionization. Based on observations made with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS 5-26555. These observations are associated with program #10505.