We used deep Very Large Array (VLA) 3 and 6 GHz radio imaging of the Hubble Frontier Field (HFF) galaxy clusters MACSJ0416-2403 and MACSJ1149+2223 to study star formation in gravitationally-lensed, intrinsically faint, high-redshift galaxies beyond the clusters. A stacking analysis is performed using μJy-level sensitivity and sub-arcsecond resolution (< 0.6") radio maps to derive the median star formation rates (SFRs) of galaxies out to z ≈ 9. Assuming Gaussian background noise levels in the stacked images allows for the calculation of SFR upper limits in these galaxies as a function of redshift. Galaxies are grouped in redshift bins 6-9 and 9-12. The upper limits for SFRs determined from the 3 GHz images as a function of redshift bin are, respectively, 66.73 and 329.30 solar masses/yr at the 3σ level. For the 6 GHz images, the SFR upper limits are, respectively, 190.71 and 705.39 solar masses/yr at the 3σ level. Our median-stacked images show only background noise rather than galaxy detections, meaning that μJy-level radio surveys are insufficient to probe the radio emission of z > 6 galaxies even after applying stacking analysis. We require deeper radio observations with R.M.S. < 1 μJy/beam from future astronomical radio facilities such as ngVLA and SKA to study the radio emission of z > 6 galaxies.