  Radio used as a star formation rate (SFR) tracer presents enormous advantages
by being unaffected by dust and radio sources being pinpointed at the
sub-arc-second level. The interpretation of the low frequency 1.4 GHz
luminosity is hampered by the difficulty in modeling the cosmic ray paths in
the interstellar medium, and their interactions with the magnetic field. In
this work, we compare the SFR derived from radio observations, and the ones
derived from spectral energy distribution (SED) modeling. We aim at better
understand the behavior of the SFR radio tracer, with a specific emphasis on
the link with star-formation histories. We used the SED modeling code Code
Investigating GALaxy Emission, CIGALE, with a non-parametric star formation
history model (SFH) and fit the data over the wavelength range from the
ultraviolet (UV) up to the mid-infrared (mid-IR). We interpret the difference
between radio and SED-based SFR tracers in the light of recent gradients in the
derived SFH. To validate the robustness of the results, we checked for any
remaining active galaxy nuclei (AGN) contribution and tested the impact of our
SFH modeling approach. Approximately 27% our galaxies present a radio SFR
(SFR$_{\rm radio}$) at least ten times larger than the instantaneous SFR from
SED-fitting (SFR$_{\rm SED}$). This trend affects primarily the galaxies that
show a declining SFH activity over the last 300 Myr. Both SFR indicators
converge toward a consistent value, when the SFHs are averaged over a period
larger than 150 Myr to derive SFR$_{\rm SED}$. Although the radio at low
frequency 1.4 GHz is a good tracer of the star formation activity of galaxies
with constant or increasing SFH, our results indicate that this is not the case
for galaxies that are quenching. Our analysis suggests that the star formation
time sensitivity of the radio low frequency could be longer than 150 Myr.
