Intense fluxes of electrons from the Earth’s radiation belt (ERB) with energies of tens and hundreds of keV can penetrate to low altitudes at low latitudes outside the South Atlantic Anomaly. This region is known as a forbidden zone of quasi-trapped energetic particles. Flux enhancements of energetic electrons in the forbidden zone, so-called forbidden energetic electrons (FEE), produce significant ionization effects in the upper atmosphere at low latitudes. In this work, solar-cycle variations of the FEE enhancements with energy > 30 keV were analyzed over a 25-year period using a database of low-orbit satellites of the NOAA/POES and MetOp series. We found the highest correlations of the annual occurrence of FEE with the F10.7 solar activity index (−0.87) and the Alfven Mach number of the upstream solar wind (0.76). Using multiparameter regression analysis, a power expression was obtained with those parameters as well as with plasma beta and the interplanetary magnetic field strength with a total correlation coefficient of 0.94. The role of the conductivity of the high-latitude ionosphere in the mechanism of the penetration of ERB electrons into the forbidden zone is discussed.