We derive the recent star formation histories (SFHs) of 23 active dwarf galaxies using Hubble Space Telescope observations from the Legacy Extragalactic UV Survey. We apply a color-magnitude diagram (CMD) fitting technique using two independent sets of stellar models, PARSEC-COLIBRI and MIST. Despite the nonnegligible recent activity, none of the 23 star-forming dwarfs show enhancements in the last 100 Myr larger than three times the 100 Myr average. The unweighted mean of the individual SFHs in the last 100 Myr is also consistent with a rather constant activity, irrespective of the atomic gas fraction. We confirm previous results that for dwarf galaxies, the CMD-based average star formation rates (SFRs) are generally higher than the FUV-based SFRs. For half of the sample, the 60 Myr average CMD-based SFR is more than two times the FUV SFR. In contrast, we find remarkable agreement between the 10 Myr average CMD-based SFR and the H alpha-based SFR. Finally, using core helium-burning stars of intermediate mass, we study the pattern of star formation spatial progression over the past 60 Myr and speculate on the possible triggers and connections of the star formation activity with the environment in which these galaxies live. Approximately half of our galaxies show spatial progression of star formation in the last 60 Myr and/or very recent diffuse and off-center activity compared to RGB stars.